International Conference on Information and Emerging Technologies (ICIET), Jun 14, 2010
These days Analog and Mixed signal (AMS) circuits are widely being designed and used in many safe... more These days Analog and Mixed signal (AMS) circuits are widely being designed and used in many safety and financial critical application domains. This fact brings the challenge of efficiently and accurately analyzing of these AMS circuits as an analysis error could result in a big financial loss. Traditionally, AMS circuits have been analyzed using paper-and-pencil proof methods or computer simulations. But these methods cannot cope with the growing complexities of AMS designs. In this paper, we propose a computer algebra system based analyzer for AMS designs. The distinguishing features of the proposed approach include its scalability, precision and automatic nature. For illustration purposes, we analyze the Impulse generator circuit using the proposed approach and compare our results with the ones obtained by simulation and paper-and-pencil proof methods.
Traditional testing techniques often reach their limits when employed for the assessment of criti... more Traditional testing techniques often reach their limits when employed for the assessment of critical Machine Control Systems as they contain a large amount of random and unpredictable components. The probabilistic analysis approach can assist in their evaluation by providing a subjective evidence of their safety and reliability. The synergy of probabilistic analysis and expressiveness of higher-order logic theorem proving results into convincing modelling and reasoning of several stringent safety cases that contribute towards the certification of high-assurance systems.
Kinematic analysis is used for trajectory planning of robotic manipulators and is an integral ste... more Kinematic analysis is used for trajectory planning of robotic manipulators and is an integral step of their design. The main idea behind kinematic analysis is to study the motion of the robot based on the geometrical relationship of the robotic links and their joints. Given the continuous nature of kinematic analysis, traditional computer-based verification methods, such as simulation, numerical methods or model checking, fail to provide reliable results. This fact makes robotic designs error prone, which may lead to disastrous consequences given the safety-critical nature of robotic applications. Leveraging upon the high expressiveness of higher-order logic, we propose to use higher-order-logic theorem proving for conducting formal kinematic analysis. As a first step towards this direction, we utilize the geometry theory of HOL-Light to develop formal reasoning support for the kinematic analysis of a two-link planar manipulator, which forms the basis for many mechanical structures in robotics. To illustrate the usefulness of our foundational formalization, we present the formal kinematic analysis of a biped walking robot.
Algebraic techniques based on Laplace transform are widely used for solving differential equation... more Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems.
The formal verification of cyber-physical systems is a challenging task mainly because of the inv... more The formal verification of cyber-physical systems is a challenging task mainly because of the involvement of various factors of continuous nature, such as the analog components or the surrounding environment. Traditional verification methods, such as model checking or automated theorem proving, usually deal with these continuous aspects by using abstracted discrete models. This fact makes cyber-physical system designs error prone, which may lead to disastrous consequences given the safety and financial critical nature of their applications. Leveraging upon the high expressiveness of higher-order logic, we propose to use higher-order-logic theorem proving to analyze continuous models of cyber-physical systems. To facilitate this process, this paper presents the formalization of the solutions of second-order homogeneous linear differential equations. To illustrate the usefulness of our foundational cyberphysical system analysis formalization, we present the formal analysis of a damped harmonic oscillator and a second-order op-amp circuit using the HOL4 theorem prover.
Simulation is the state-of-the-art analysis technique for distributed thermal management schemes.... more Simulation is the state-of-the-art analysis technique for distributed thermal management schemes. Due to the numerous parameters involved and the distributed nature of these schemes, such non-exhaustive verification may fail to catch functional bugs in the algorithm or may report misleading performance characteristics. To overcome these limitations, we propose a methodology to perform formal verification of distributed dynamic thermal management for many-core systems. The proposed methodology is based on the SPIN model checker and the Lamport timestamps algorithm. Our methodology allows specification and verification of both functional and timing properties in a distributed many-core system. In order to illustrate the applicability and benefits of our methodology, we perform a case study on a state-of-the-art agent-based distributed thermal management scheme.
Relays are widely used in power distribution systems to isolate their faulty components and thus ... more Relays are widely used in power distribution systems to isolate their faulty components and thus avoid disruption of power and damaging expensive equipment. The reliability of relay-based protection of power distribution systems is of utmost importance and is judged by first constructing Markovian models of individual modules and then analyzing these models analytically or using simulation. However, due to their inherent limitations, simulations and analytical methods cannot ascertain accurate results and are not scalable, respectively. To overcome these limitations, we propose a modular approach for developing Markovian models of relay-based protected components and then analyzing the reliability of the overall power distribution system by executing its individual modules in parallel using the PRISM probabilistic model checker. The paper presents a foundational model for a relay-based protected component that can be incrementally updated to represent more advanced behaviors, such as self-checking, routine test and continuous monitoring. Moreover, the paper provides a set of reliability assessment properties of power distribution systems that can be formally verified by PRISM. For illustration purposes, we present the analysis of a typical power distribution substation.
The accuracy of control systems analysis is of paramount importance as even minor design errors c... more The accuracy of control systems analysis is of paramount importance as even minor design errors can lead to disastrous consequences in this domain. This paper provides a higher-order-logic theorem proving based framework for the formal analysis of steady state errors in feedback control systems. In particular, we present the formalization of control system foundations, like transfer functions, summing junctions, feedback loops and pickoff points, and steady state error models for the step, ramp and parabola cases. These foundations can be built upon to formally specify a wide range of feedback control systems in higher-order logic and reason about their steady state errors within the sound core of a theorem prover. The proposed formalization is based on the complex number theory of the HOL-Light theorem prover. For illustration purposes, we present the steady state error analysis of a solar tracking control system.
Nowadays, computer simulation is one of the most widely used performance analysis technique. Howe... more Nowadays, computer simulation is one of the most widely used performance analysis technique. However, simulation based analysis usually provides approximate results due to its inherent nature and it cannot handle large-scale problems due to its enormous CPU time requirements. The unreliability of the results poses a serious problem in safety critical applications, such as those in space travel, military, and medicine, where a mismatch between the predicted and the actual system performance may result in either inefficient usage of the available resources or by unnecessarily paying higher costs to meet some performance or reliability criteria. A possible solution for overcoming these limitations is to conduct performance analysis within the environment of a higher-order-logic theorem prover. Higher-order logic is a system of deduction with a precise semantics and can be used for the development of almost all classical mathematical theories. Whereas, interactive theorem proving is the field of computer science and mathematical logic concerned with computer based formal proof tools that require some sort of human assistance. Due to the high expressiveness of the higher-order-logic and the inherent soundness of interactive theorem proving, this approach can be used to conduct error free performance analysis at the cost of significant user interaction.
Information theory is widely used in a very broad class of scientific and engineering problems, i... more Information theory is widely used in a very broad class of scientific and engineering problems, including cryptography, neurobiology, quantum computing, plagiarism detection and other forms of data analysis. Despite the safety-critical nature of some of these applications, most of the information theoretic analysis is done using informal techniques and thus cannot be completely relied upon. To facilitate the formal reasoning about information theoretic aspects, this paper presents a rigorous higher-order logic formalization of some of the most widely used information theoretic principles. Building on fundamental formalizations of measure and Lebesgue integration theories for extended reals, we formalize the Radon-Nikodym derivative and prove some of its properties using the HOL theorem prover. This infrastructure is then used to formalize information theoretic fundamentals like Shannon entropy and relative entropy. We discuss potential applications of the proposed formalization for the analysis of data compression and security protocols.
Reliability analysis of combinational circuits has become imperative these days due to the extens... more Reliability analysis of combinational circuits has become imperative these days due to the extensive usage of nanotechnologies in their fabrication. Traditionally, reliability analysis of combinational circuits is done using simulation or paper-and-pencil proof methods. But, these techniques do not ensure accurate results and thus may lead to disastrous consequences when dealing with safety critical applications. In this paper, we mainly tackle the accuracy problem of reliability analysis by presenting a formal reliability analysis approach that is based on higher-order-logic theorem proving. The distinguishing feature of the approach is that, despite being based on higher-order logic that is undecidable, it is capable of automatically evaluating the precise reliability of combinational circuits. The paper summarizes the formalization infrastructure that is fundamental to our approach. For illustration purposes, it also presents the reliability analysis of a few benchmark combinational circuits.
Optical systems are becoming increasingly important as they tend to resolve many bottlenecks in t... more Optical systems are becoming increasingly important as they tend to resolve many bottlenecks in the present age communications and electronics. Some common examples include their usage to meet high capacity link demands in communication systems and to overcome the performance limitations of metal interconnect in silicon chips. Though, the inability to efficiently analyze optical systems using traditional analysis approaches, due to the continuous nature of optics, somewhat limits their application, specially in safety-critical applications. In order to overcome this limitation, we propose to formally analyze optical systems using a higher-order-logic theorem prover (HOL). As a first step in this endeavor, we formally analyze eigenvalues for planar optical waveguides, which are some of the most fundamental components in optical devices. For the formalization, we have utilized the mathematical concepts of differentiation of piecewise functions and one-sided limits of functions. In order to illustrate the practical effectiveness of our results, we present the formal analysis of a planar asymmetric waveguide.
In the field of probabilistic analysis, the concept of conditional probability plays a major role... more In the field of probabilistic analysis, the concept of conditional probability plays a major role for estimating probabilities when some partial information concerning the result of the experiment is available. This paper presents a higher-order-logic definition of conditional probability and the formal verification of some classical properties of conditional probability, such as, the total probability law and Bayes' theorem. This infrastructure, implemented in the HOL theorem prover, allows us to precisely reason about conditional probabilities for probabilistic systems within the sound core of HOL and thus proves to be quite useful for the analysis of systems used in safety-critical domains, such as space, medicine and transportation. To demonstrate the usefulness of our approach, we provide the precise probabilistic analysis of the binary asymmetric channel, a widely used concept in communication theory, within the HOL theorem prover.
These days Analog and Mixed signal (AMS) circuits are widely being designed and used in many safe... more These days Analog and Mixed signal (AMS) circuits are widely being designed and used in many safety and financial critical application domains. This fact brings the challenge of efficiently and accurately analyzing these AMS circuits as an analysis error could result in a big financial loss. Traditionally, AMS circuits have been analyzed using paper-and-pencil proof methods or computer simulations. But these methods cannot cope with the growing complexities of AMS designs. In this paper, we propose a computer algebra system based analyzer for AMS designs. The distinguishing features of the proposed approach include its scalability, precision and automatic nature. For illustration purposes, we analyze the Impulse generator circuit using the proposed approach and compare our results with the ones obtained by simulation and paper-and-pencil proof methods.
Automated Technology for Verification and …, Jan 1, 2011
The mathematical concept of Markov chains is widely used to model and analyze many engineering an... more The mathematical concept of Markov chains is widely used to model and analyze many engineering and scientific problems. Markovian models are usually analyzed using computer simulation, and more recently using probabilistic model-checking but these methods either do not guarantee accurate analysis or are not scalable. As an alternative, we propose to use higher-order-logic theorem proving to reason about properties of systems that can be described as Markov chains. As the first step towards this goal, this paper presents a formalization of time homogeneous finite-state Discrete-time Markov chains and the formal verification of some of their fundamental properties, such as Joint probabilities, Chapman-Kolmogorov equation and steady state probabilities, using the HOL theorem prover. For illustration purposes, we utilize our formalization to analyze a simplified binary communication channel.
Real-time systems usually involve a subtle interaction of a number of distributed components and ... more Real-time systems usually involve a subtle interaction of a number of distributed components and have a high degree of parallelism, which makes their performance analysis quite complex. Thus, traditional techniques, such as simulation, fail to produce reasonable results. Formal methods pose an interesting solution but they usually lack the capabilities to reason about quantitative time and probabilistic properties, which play a vital role in performance analysis. This paper addresses this issue by presenting a formal approach for assessing the performance of a real-time system. To describe the evolution of the system, we use a real-time rewriting logic, in which we mechanize the extraction of quantitative information from a timed model. To evaluate the performance, we first consider the set of runs obtained from different initial input values that are not equivalent modulo the equational theory associated with the model. The overall performance of the system is then evaluated as the performance of each run weighted by its probability mass function. In order to illustrate the practical effectiveness of the proposed approach, we present the formal modeling and performance analysis of a simple search engine.
… Control Systems: Applications for Flexibility and …, Jan 1, 2010
Until the last decade, real-time systems were analyzed using traditional techniques, such as pape... more Until the last decade, real-time systems were analyzed using traditional techniques, such as paper-and-pencil proof methods or simulation. The paper-and-pencil based proof techniques usually have some risk of an erroneous analysis due to the human-error factor. Similarly, ...
Journal of Computer Science and Technology, Jan 1, 2010
Probabilistic techniques are widely used in the analysis of algorithms to estimate the computatio... more Probabilistic techniques are widely used in the analysis of algorithms to estimate the computational complexity of algorithms or a computational problem. Traditionally, such analyses are performed using paper-and-pencil proofs and the results are sometimes validated using simulation techniques. These techniques are informal and thus may result in an inaccurate analysis. In this paper, we propose a formal technique for analyzing the expected time complexity of algorithms using higher-order-logic theorem proving. The approach calls for mathematically modeling the algorithm along with its inputs, using indicator random variables, in higher-order logic. This model is then used to formally reason about the expected time complexity of the underlying algorithm in a theorem prover. The paper includes the higher-order-logic formalization of indicator random variables, which are fundamental to the proposed infrastructure. In order to illustrate the practical effectiveness and utilization of the proposed infrastructure, the paper also includes the analysis of algorithms for three well-known problems, i.e., the hat-check problem, the birthday paradox and the hiring problem.
Continuous random variables are widely used to mathematically describe random phenomenon in engin... more Continuous random variables are widely used to mathematically describe random phenomenon in engineering and physical sciences. In this paper, we present a higher-order logic formalization of the Standard Uniform random variable. We show the correctness of this specification by proving the corresponding probability distribution properties within the HOL theorem prover and the proof steps have been summarized. This formalized Standard Uniform random variable can be transformed to formalize other continuous random variables, such as Uniform, Exponential, Normal, etc., by using various Non-uniform random number generation techniques. The formalization of these continuous random variables will enable us to perform error free probabilistic analysis of systems within the framework of a higher-order-logic theorem prover. For illustration purposes, we present the formalization of the Continuous Uniform random variable based on our Standard Uniform random variable and then utilize it to perform a simple probabilistic analysis of roundoff error in HOL.
International Conference on Information and Emerging Technologies (ICIET), Jun 14, 2010
These days Analog and Mixed signal (AMS) circuits are widely being designed and used in many safe... more These days Analog and Mixed signal (AMS) circuits are widely being designed and used in many safety and financial critical application domains. This fact brings the challenge of efficiently and accurately analyzing of these AMS circuits as an analysis error could result in a big financial loss. Traditionally, AMS circuits have been analyzed using paper-and-pencil proof methods or computer simulations. But these methods cannot cope with the growing complexities of AMS designs. In this paper, we propose a computer algebra system based analyzer for AMS designs. The distinguishing features of the proposed approach include its scalability, precision and automatic nature. For illustration purposes, we analyze the Impulse generator circuit using the proposed approach and compare our results with the ones obtained by simulation and paper-and-pencil proof methods.
Traditional testing techniques often reach their limits when employed for the assessment of criti... more Traditional testing techniques often reach their limits when employed for the assessment of critical Machine Control Systems as they contain a large amount of random and unpredictable components. The probabilistic analysis approach can assist in their evaluation by providing a subjective evidence of their safety and reliability. The synergy of probabilistic analysis and expressiveness of higher-order logic theorem proving results into convincing modelling and reasoning of several stringent safety cases that contribute towards the certification of high-assurance systems.
Kinematic analysis is used for trajectory planning of robotic manipulators and is an integral ste... more Kinematic analysis is used for trajectory planning of robotic manipulators and is an integral step of their design. The main idea behind kinematic analysis is to study the motion of the robot based on the geometrical relationship of the robotic links and their joints. Given the continuous nature of kinematic analysis, traditional computer-based verification methods, such as simulation, numerical methods or model checking, fail to provide reliable results. This fact makes robotic designs error prone, which may lead to disastrous consequences given the safety-critical nature of robotic applications. Leveraging upon the high expressiveness of higher-order logic, we propose to use higher-order-logic theorem proving for conducting formal kinematic analysis. As a first step towards this direction, we utilize the geometry theory of HOL-Light to develop formal reasoning support for the kinematic analysis of a two-link planar manipulator, which forms the basis for many mechanical structures in robotics. To illustrate the usefulness of our foundational formalization, we present the formal kinematic analysis of a biped walking robot.
Algebraic techniques based on Laplace transform are widely used for solving differential equation... more Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems.
The formal verification of cyber-physical systems is a challenging task mainly because of the inv... more The formal verification of cyber-physical systems is a challenging task mainly because of the involvement of various factors of continuous nature, such as the analog components or the surrounding environment. Traditional verification methods, such as model checking or automated theorem proving, usually deal with these continuous aspects by using abstracted discrete models. This fact makes cyber-physical system designs error prone, which may lead to disastrous consequences given the safety and financial critical nature of their applications. Leveraging upon the high expressiveness of higher-order logic, we propose to use higher-order-logic theorem proving to analyze continuous models of cyber-physical systems. To facilitate this process, this paper presents the formalization of the solutions of second-order homogeneous linear differential equations. To illustrate the usefulness of our foundational cyberphysical system analysis formalization, we present the formal analysis of a damped harmonic oscillator and a second-order op-amp circuit using the HOL4 theorem prover.
Simulation is the state-of-the-art analysis technique for distributed thermal management schemes.... more Simulation is the state-of-the-art analysis technique for distributed thermal management schemes. Due to the numerous parameters involved and the distributed nature of these schemes, such non-exhaustive verification may fail to catch functional bugs in the algorithm or may report misleading performance characteristics. To overcome these limitations, we propose a methodology to perform formal verification of distributed dynamic thermal management for many-core systems. The proposed methodology is based on the SPIN model checker and the Lamport timestamps algorithm. Our methodology allows specification and verification of both functional and timing properties in a distributed many-core system. In order to illustrate the applicability and benefits of our methodology, we perform a case study on a state-of-the-art agent-based distributed thermal management scheme.
Relays are widely used in power distribution systems to isolate their faulty components and thus ... more Relays are widely used in power distribution systems to isolate their faulty components and thus avoid disruption of power and damaging expensive equipment. The reliability of relay-based protection of power distribution systems is of utmost importance and is judged by first constructing Markovian models of individual modules and then analyzing these models analytically or using simulation. However, due to their inherent limitations, simulations and analytical methods cannot ascertain accurate results and are not scalable, respectively. To overcome these limitations, we propose a modular approach for developing Markovian models of relay-based protected components and then analyzing the reliability of the overall power distribution system by executing its individual modules in parallel using the PRISM probabilistic model checker. The paper presents a foundational model for a relay-based protected component that can be incrementally updated to represent more advanced behaviors, such as self-checking, routine test and continuous monitoring. Moreover, the paper provides a set of reliability assessment properties of power distribution systems that can be formally verified by PRISM. For illustration purposes, we present the analysis of a typical power distribution substation.
The accuracy of control systems analysis is of paramount importance as even minor design errors c... more The accuracy of control systems analysis is of paramount importance as even minor design errors can lead to disastrous consequences in this domain. This paper provides a higher-order-logic theorem proving based framework for the formal analysis of steady state errors in feedback control systems. In particular, we present the formalization of control system foundations, like transfer functions, summing junctions, feedback loops and pickoff points, and steady state error models for the step, ramp and parabola cases. These foundations can be built upon to formally specify a wide range of feedback control systems in higher-order logic and reason about their steady state errors within the sound core of a theorem prover. The proposed formalization is based on the complex number theory of the HOL-Light theorem prover. For illustration purposes, we present the steady state error analysis of a solar tracking control system.
Nowadays, computer simulation is one of the most widely used performance analysis technique. Howe... more Nowadays, computer simulation is one of the most widely used performance analysis technique. However, simulation based analysis usually provides approximate results due to its inherent nature and it cannot handle large-scale problems due to its enormous CPU time requirements. The unreliability of the results poses a serious problem in safety critical applications, such as those in space travel, military, and medicine, where a mismatch between the predicted and the actual system performance may result in either inefficient usage of the available resources or by unnecessarily paying higher costs to meet some performance or reliability criteria. A possible solution for overcoming these limitations is to conduct performance analysis within the environment of a higher-order-logic theorem prover. Higher-order logic is a system of deduction with a precise semantics and can be used for the development of almost all classical mathematical theories. Whereas, interactive theorem proving is the field of computer science and mathematical logic concerned with computer based formal proof tools that require some sort of human assistance. Due to the high expressiveness of the higher-order-logic and the inherent soundness of interactive theorem proving, this approach can be used to conduct error free performance analysis at the cost of significant user interaction.
Information theory is widely used in a very broad class of scientific and engineering problems, i... more Information theory is widely used in a very broad class of scientific and engineering problems, including cryptography, neurobiology, quantum computing, plagiarism detection and other forms of data analysis. Despite the safety-critical nature of some of these applications, most of the information theoretic analysis is done using informal techniques and thus cannot be completely relied upon. To facilitate the formal reasoning about information theoretic aspects, this paper presents a rigorous higher-order logic formalization of some of the most widely used information theoretic principles. Building on fundamental formalizations of measure and Lebesgue integration theories for extended reals, we formalize the Radon-Nikodym derivative and prove some of its properties using the HOL theorem prover. This infrastructure is then used to formalize information theoretic fundamentals like Shannon entropy and relative entropy. We discuss potential applications of the proposed formalization for the analysis of data compression and security protocols.
Reliability analysis of combinational circuits has become imperative these days due to the extens... more Reliability analysis of combinational circuits has become imperative these days due to the extensive usage of nanotechnologies in their fabrication. Traditionally, reliability analysis of combinational circuits is done using simulation or paper-and-pencil proof methods. But, these techniques do not ensure accurate results and thus may lead to disastrous consequences when dealing with safety critical applications. In this paper, we mainly tackle the accuracy problem of reliability analysis by presenting a formal reliability analysis approach that is based on higher-order-logic theorem proving. The distinguishing feature of the approach is that, despite being based on higher-order logic that is undecidable, it is capable of automatically evaluating the precise reliability of combinational circuits. The paper summarizes the formalization infrastructure that is fundamental to our approach. For illustration purposes, it also presents the reliability analysis of a few benchmark combinational circuits.
Optical systems are becoming increasingly important as they tend to resolve many bottlenecks in t... more Optical systems are becoming increasingly important as they tend to resolve many bottlenecks in the present age communications and electronics. Some common examples include their usage to meet high capacity link demands in communication systems and to overcome the performance limitations of metal interconnect in silicon chips. Though, the inability to efficiently analyze optical systems using traditional analysis approaches, due to the continuous nature of optics, somewhat limits their application, specially in safety-critical applications. In order to overcome this limitation, we propose to formally analyze optical systems using a higher-order-logic theorem prover (HOL). As a first step in this endeavor, we formally analyze eigenvalues for planar optical waveguides, which are some of the most fundamental components in optical devices. For the formalization, we have utilized the mathematical concepts of differentiation of piecewise functions and one-sided limits of functions. In order to illustrate the practical effectiveness of our results, we present the formal analysis of a planar asymmetric waveguide.
In the field of probabilistic analysis, the concept of conditional probability plays a major role... more In the field of probabilistic analysis, the concept of conditional probability plays a major role for estimating probabilities when some partial information concerning the result of the experiment is available. This paper presents a higher-order-logic definition of conditional probability and the formal verification of some classical properties of conditional probability, such as, the total probability law and Bayes' theorem. This infrastructure, implemented in the HOL theorem prover, allows us to precisely reason about conditional probabilities for probabilistic systems within the sound core of HOL and thus proves to be quite useful for the analysis of systems used in safety-critical domains, such as space, medicine and transportation. To demonstrate the usefulness of our approach, we provide the precise probabilistic analysis of the binary asymmetric channel, a widely used concept in communication theory, within the HOL theorem prover.
These days Analog and Mixed signal (AMS) circuits are widely being designed and used in many safe... more These days Analog and Mixed signal (AMS) circuits are widely being designed and used in many safety and financial critical application domains. This fact brings the challenge of efficiently and accurately analyzing these AMS circuits as an analysis error could result in a big financial loss. Traditionally, AMS circuits have been analyzed using paper-and-pencil proof methods or computer simulations. But these methods cannot cope with the growing complexities of AMS designs. In this paper, we propose a computer algebra system based analyzer for AMS designs. The distinguishing features of the proposed approach include its scalability, precision and automatic nature. For illustration purposes, we analyze the Impulse generator circuit using the proposed approach and compare our results with the ones obtained by simulation and paper-and-pencil proof methods.
Automated Technology for Verification and …, Jan 1, 2011
The mathematical concept of Markov chains is widely used to model and analyze many engineering an... more The mathematical concept of Markov chains is widely used to model and analyze many engineering and scientific problems. Markovian models are usually analyzed using computer simulation, and more recently using probabilistic model-checking but these methods either do not guarantee accurate analysis or are not scalable. As an alternative, we propose to use higher-order-logic theorem proving to reason about properties of systems that can be described as Markov chains. As the first step towards this goal, this paper presents a formalization of time homogeneous finite-state Discrete-time Markov chains and the formal verification of some of their fundamental properties, such as Joint probabilities, Chapman-Kolmogorov equation and steady state probabilities, using the HOL theorem prover. For illustration purposes, we utilize our formalization to analyze a simplified binary communication channel.
Real-time systems usually involve a subtle interaction of a number of distributed components and ... more Real-time systems usually involve a subtle interaction of a number of distributed components and have a high degree of parallelism, which makes their performance analysis quite complex. Thus, traditional techniques, such as simulation, fail to produce reasonable results. Formal methods pose an interesting solution but they usually lack the capabilities to reason about quantitative time and probabilistic properties, which play a vital role in performance analysis. This paper addresses this issue by presenting a formal approach for assessing the performance of a real-time system. To describe the evolution of the system, we use a real-time rewriting logic, in which we mechanize the extraction of quantitative information from a timed model. To evaluate the performance, we first consider the set of runs obtained from different initial input values that are not equivalent modulo the equational theory associated with the model. The overall performance of the system is then evaluated as the performance of each run weighted by its probability mass function. In order to illustrate the practical effectiveness of the proposed approach, we present the formal modeling and performance analysis of a simple search engine.
… Control Systems: Applications for Flexibility and …, Jan 1, 2010
Until the last decade, real-time systems were analyzed using traditional techniques, such as pape... more Until the last decade, real-time systems were analyzed using traditional techniques, such as paper-and-pencil proof methods or simulation. The paper-and-pencil based proof techniques usually have some risk of an erroneous analysis due to the human-error factor. Similarly, ...
Journal of Computer Science and Technology, Jan 1, 2010
Probabilistic techniques are widely used in the analysis of algorithms to estimate the computatio... more Probabilistic techniques are widely used in the analysis of algorithms to estimate the computational complexity of algorithms or a computational problem. Traditionally, such analyses are performed using paper-and-pencil proofs and the results are sometimes validated using simulation techniques. These techniques are informal and thus may result in an inaccurate analysis. In this paper, we propose a formal technique for analyzing the expected time complexity of algorithms using higher-order-logic theorem proving. The approach calls for mathematically modeling the algorithm along with its inputs, using indicator random variables, in higher-order logic. This model is then used to formally reason about the expected time complexity of the underlying algorithm in a theorem prover. The paper includes the higher-order-logic formalization of indicator random variables, which are fundamental to the proposed infrastructure. In order to illustrate the practical effectiveness and utilization of the proposed infrastructure, the paper also includes the analysis of algorithms for three well-known problems, i.e., the hat-check problem, the birthday paradox and the hiring problem.
Continuous random variables are widely used to mathematically describe random phenomenon in engin... more Continuous random variables are widely used to mathematically describe random phenomenon in engineering and physical sciences. In this paper, we present a higher-order logic formalization of the Standard Uniform random variable. We show the correctness of this specification by proving the corresponding probability distribution properties within the HOL theorem prover and the proof steps have been summarized. This formalized Standard Uniform random variable can be transformed to formalize other continuous random variables, such as Uniform, Exponential, Normal, etc., by using various Non-uniform random number generation techniques. The formalization of these continuous random variables will enable us to perform error free probabilistic analysis of systems within the framework of a higher-order-logic theorem prover. For illustration purposes, we present the formalization of the Continuous Uniform random variable based on our Standard Uniform random variable and then utilize it to perform a simple probabilistic analysis of roundoff error in HOL.
Reliable transferring of data from one clock domain to another requires synchronization. Therefor... more Reliable transferring of data from one clock domain to another requires synchronization. Therefore, synchronizers play an important role in clock domain crossing (CDC). But despite their wide applications, there is no standard quantitative metric available to analyze various synchronizer configurations on common grounds. To overcome this limitation, this paper presents a comparison of three basic and widely used synchronizers. Latency and power consumption metric are measured for level, edge-detecting and pulse generating synchronizers. Furthermore, effects of these synchronizers are studied when applied to some commonly used asynchronous handshaking protocols under 90nm CMOS technology.
Uploads
Papers by osman hasan