... Reification was carried out to a state machine representation, and then to a hardware block m... more ... Reification was carried out to a state machine representation, and then to a hardware block model described in LCF LSM and Ella, a logic description language for hardware. ... 6. WJ Cullyer and CH Pygott, Hardware proofs using LCF-LSM and ELLA. In: RSRE Memorandum No. ...
Examined is a methodology for hardware verification developed by Royal Signals and Radar Establis... more Examined is a methodology for hardware verification developed by Royal Signals and Radar Establishment (RSRE) in the context of the SRI International's Enhanced Hierarchical Design Methodology (EHDM) specification/verification system. The methodology utilizes a four-level specification hierarchy with the following levels: functional level, finite automata model, block model, and circuit level. The properties of a level are proved as theorems in the level below it. This methodology is applied to a 6-bit counter problem and is critically examined. The specifications are written in EHDM's specification language, Extended Special, and the proofs are improving both the RSRE methodology and the EHDM system.
A preliminary design for a validation experiment has been developed that addresses several proble... more A preliminary design for a validation experiment has been developed that addresses several problems that are unique to assuring the extremely high quality of multiple version programs in process control software. If successful, the experimental procedure tests the programs in a realistic manner; it makes a minimum number of assumptions; and it is more efficient than natural life testing. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process control testing,, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level by using confidence intervals obtained for the transition probabilities during th...
Semi-Markov processes are increasingly being used in the modeling of complex reconfigurable syste... more Semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault-tolerant computers). The estimation of system reliability reduces to solving the model for its state probabilities. When decomposition into smaller sub-models is possible, solving the decomposed models and joining the solutions has several advantages, including lower computational cost and more stable numerical properties. Interesting cases arise when non-failure states of the subsystems can be system failure modes. A technique is proposed to combine information about the sub-models to estimate this additional probability. This question is considered in the framework of Semi-Markov processes whose transition densities have a rational Laplace transform. We state a theorem that characterizes in a simple fashion when these transforms exist, and prove as a special case that the transforms always exist when no " instantaneous jumps " are present. When there are no instanta...
Examined is a methodology for hardware verification developed by Royal Signals and Radar Establis... more Examined is a methodology for hardware verification developed by Royal Signals and Radar Establishment (RSRE) in the context of the SRI International's Enhanced Hierarchical Design Methodology (EHDM) specification/verification system. The methodology utilizes a four-level specification hierarchy with the following levels: functional level, finite automata model, block model, and circuit level. The properties of a level are proved as theorems in the level below it. This methodology is applied to a 6-bit counter problem and is critically examined. The specifications are written in EHDM's specification language, Extended Special, and the proofs are improving both the RSRE methodology and the EHDM system.
Preliminary design developed for validation experiment that addresses problems unique to assuring... more Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
Fully Adaptive Radar and Waveform Design , with benefit: Spectral Dominance, enhanced Radar resol... more Fully Adaptive Radar and Waveform Design , with benefit: Spectral Dominance, enhanced Radar resolution, EW Countermeasures Operator Formalism to Represent Image-from-Data Process with benefit Adaptability to Sensing Modalities and Geometry, Flexibility of Mathematical Image Solution Methods Sensing in Target Identification: Analysis/Synthesis of Invariants with benefit Fast classification of objects with high dependability. Non GPS-based Navigation and Geo-location with benefit Navigation, location and targeting anywhere, with GPS precision. The culture of signals engineering and mathematics are historically intertwined, should reinforce each other all the more in future. Multi-Dimensional Diverse Waveform Design for Multi-Antenna Sensing & Surveillance Systems; Noise Radar Implementing Compressive Sensing ; Thermal Light “Ghost Imaging” . Future of Synthetic Aperture Radar: Multi-function, robust, agile, adaptive system with performance guarantees operate in complex, rapidly varyin...
Numerous applications in the area of computer system analysis can be effectively studied with Mar... more Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the evolutionary behavior of the computer system by a continuous-time Markov chain, and a reward rate is associated with each state. In reliability/availability models, upstates have reward rate 1, and down states have reward rate zero associated with them. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Steady-state expected reward rate and expected instantaneous reward rate are clearly useful measures which can be extracted from the Markov reward model. The diversity of areas where Markov reward models may be used is illustrated with a comparative study of three examples of interest to the fault tolerant computing community.
Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, ... more Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, which use tools from the topology of real manifolds. Simpler proofs were discovered in the new century, of the Hilbert Nullstellensatz, and the Gelfand-Mazur Theorem. We give a related proof that an irreducible real polynomial has degree 2 or less, Gauss's form of the Fundamental Theorem of Algebra. It has been debated whether an elementary proof for FTA can be found, using the Brouwer Fixed-Point Theorem as its "analytical" component. In the present case the analytic or topological tool employed is Brouwer's Theorem on Invariance of Domain, which derives from his Fixed-Point Theorem. A corollary of Domain Invariance is that an injective mapping of one compact manifold to another (connected) one of the same dimension, is in fact surjective and a homeomorphism. The desired result (FTA) comes from the fact that a real sphere and its (quotient) projective space of the same...
An adolescent version of Lebesgue theory considers countable subsets of the real numbers. A funct... more An adolescent version of Lebesgue theory considers countable subsets of the real numbers. A function which is right-continuous "nearly always" (except for countably many) is also continuous nearly always. A function with either a right-hand or a left-hand derivative existing nearly always, is differentiable nearly always. This is a stronger result than presented in classical texts. To deal with a higher one-sided derivative, the Taylor "jet" approach is suggested, and hints are given for an Internal Set Theory generalization, replacing limits by arithmetic in non-Standard real numbers.
A closed-form formula for all the Fibonacci numbers, conjectured by the electrical engineer S.D. ... more A closed-form formula for all the Fibonacci numbers, conjectured by the electrical engineer S.D. Bedrosian, is described and proven by two distinct methods. The first method illustrates several principles of analysis and linear algebra, and is ideal for classroom explanation of an unexpected result that can be verified using calculators. The proof does not use complex numbers or algebraic equations, the Binet formula, generating functions, or resultant constructions. It does use the addition law of the sine and cosine, the relation between the set of eigenvalues (where these are simple and distinct) and the determinant,, and the Laplace expansion. The second proof was provided at one sitting by an anonymous geometer, and uses complex numbers, roots of unity, and the Binet formula,
The Maximum Principle from elliptic PDE has a simple constructive proof. This proof in fact leads... more The Maximum Principle from elliptic PDE has a simple constructive proof. This proof in fact leads to a factorization of any real polynomial whose degree is 3 or greater, the Fundamental Theorem of Algebra. The reciprocal polynomial function leads to two harmonic functions of two variables conjugate to each other and continuous everywhere. This leads to a contradiction with the Maximum Principle applied to a perturbed function. The technique is basically an analytic version of work of R. Redheffer from the 1950s, which gave more of a formal and combinatorial impression.
Proceedings of the 2012 ACM Research in Applied Computation Symposium on - RACS '12, 2012
The Polynomial method described in has been implemented for the non-singular rational square matr... more The Polynomial method described in has been implemented for the non-singular rational square matrix A for the computation of e At using the P-adic arithmetic software package---Exact Scientific Computational Library (ESCL) which we have developed. During the calculation process, truncation error is completely avoided. Efficiency comparisons have been investigated with direct summation, P-adic integer and P-adic long-integer data type representations .
International Journal of Networked and Distributed Computing, 2013
A P-adic Exact Scientific Computational Library (ESCL) for rational matrix operations has been de... more A P-adic Exact Scientific Computational Library (ESCL) for rational matrix operations has been developed over the past few years. The effort has been focusing on converting all rational number operations to integer calculation, and fully taking advantage of the fast integer multiplication of modern computer architectures. In this paper, we report our progress on parallel implementation of P-adic arithmetic by means of a multiple modulus rational system related to the Chinese remainder theorem. Experimental results are given to illustrate computational efficiency.
Hensel code was originally defined by Krishnamurthy, Rao and Subramanian [1], which was developed... more Hensel code was originally defined by Krishnamurthy, Rao and Subramanian [1], which was developed from the P-adic number system first proposed by Hensel in 1900s. The purpose was to realize exact computation for rational numbers. The Hensel code arithmetic has been well developed [1, 2, 3], but the problem of detecting Hensel code overflow and underflow has not been properly addressed . In this paper, we proposed a method for Hensel code overflow detection. The method can realize overflow detection by the prime p and the Hensel code itself. Using this method, a few digits of the Hensel code will be sacrificed.
ABSTRACT Automatic target recognition, or target discrimination, is an ever-increasing need in bo... more ABSTRACT Automatic target recognition, or target discrimination, is an ever-increasing need in both tactical and strategic engage-ments. Complex imaging systems, such as those based on adaptive optics compensation, are proven but expensive. This paper addresses a specific problem amenable to non-imaging distinction of targets, specifically symmetric and oblong. The approach is to illuminate a target with a rotating oblong beam, either in the near field (tactical) or far field (strate-gic). The returns from a symmetric object in the absence of pointing errors will be constant while returns from an oblong object will produce a sinusoidal signal, thus distinguishing the objects without imaging. This paper addresses the result of illumination with an oblong beam, starting with a pure beam, a beam corrupted by atmospheric effects and a beam affected by pointing errors referred to as jitter and boresight.
... Reification was carried out to a state machine representation, and then to a hardware block m... more ... Reification was carried out to a state machine representation, and then to a hardware block model described in LCF LSM and Ella, a logic description language for hardware. ... 6. WJ Cullyer and CH Pygott, Hardware proofs using LCF-LSM and ELLA. In: RSRE Memorandum No. ...
Examined is a methodology for hardware verification developed by Royal Signals and Radar Establis... more Examined is a methodology for hardware verification developed by Royal Signals and Radar Establishment (RSRE) in the context of the SRI International's Enhanced Hierarchical Design Methodology (EHDM) specification/verification system. The methodology utilizes a four-level specification hierarchy with the following levels: functional level, finite automata model, block model, and circuit level. The properties of a level are proved as theorems in the level below it. This methodology is applied to a 6-bit counter problem and is critically examined. The specifications are written in EHDM's specification language, Extended Special, and the proofs are improving both the RSRE methodology and the EHDM system.
A preliminary design for a validation experiment has been developed that addresses several proble... more A preliminary design for a validation experiment has been developed that addresses several problems that are unique to assuring the extremely high quality of multiple version programs in process control software. If successful, the experimental procedure tests the programs in a realistic manner; it makes a minimum number of assumptions; and it is more efficient than natural life testing. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process control testing,, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level by using confidence intervals obtained for the transition probabilities during th...
Semi-Markov processes are increasingly being used in the modeling of complex reconfigurable syste... more Semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault-tolerant computers). The estimation of system reliability reduces to solving the model for its state probabilities. When decomposition into smaller sub-models is possible, solving the decomposed models and joining the solutions has several advantages, including lower computational cost and more stable numerical properties. Interesting cases arise when non-failure states of the subsystems can be system failure modes. A technique is proposed to combine information about the sub-models to estimate this additional probability. This question is considered in the framework of Semi-Markov processes whose transition densities have a rational Laplace transform. We state a theorem that characterizes in a simple fashion when these transforms exist, and prove as a special case that the transforms always exist when no " instantaneous jumps " are present. When there are no instanta...
Examined is a methodology for hardware verification developed by Royal Signals and Radar Establis... more Examined is a methodology for hardware verification developed by Royal Signals and Radar Establishment (RSRE) in the context of the SRI International's Enhanced Hierarchical Design Methodology (EHDM) specification/verification system. The methodology utilizes a four-level specification hierarchy with the following levels: functional level, finite automata model, block model, and circuit level. The properties of a level are proved as theorems in the level below it. This methodology is applied to a 6-bit counter problem and is critically examined. The specifications are written in EHDM's specification language, Extended Special, and the proofs are improving both the RSRE methodology and the EHDM system.
Preliminary design developed for validation experiment that addresses problems unique to assuring... more Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
Fully Adaptive Radar and Waveform Design , with benefit: Spectral Dominance, enhanced Radar resol... more Fully Adaptive Radar and Waveform Design , with benefit: Spectral Dominance, enhanced Radar resolution, EW Countermeasures Operator Formalism to Represent Image-from-Data Process with benefit Adaptability to Sensing Modalities and Geometry, Flexibility of Mathematical Image Solution Methods Sensing in Target Identification: Analysis/Synthesis of Invariants with benefit Fast classification of objects with high dependability. Non GPS-based Navigation and Geo-location with benefit Navigation, location and targeting anywhere, with GPS precision. The culture of signals engineering and mathematics are historically intertwined, should reinforce each other all the more in future. Multi-Dimensional Diverse Waveform Design for Multi-Antenna Sensing & Surveillance Systems; Noise Radar Implementing Compressive Sensing ; Thermal Light “Ghost Imaging” . Future of Synthetic Aperture Radar: Multi-function, robust, agile, adaptive system with performance guarantees operate in complex, rapidly varyin...
Numerous applications in the area of computer system analysis can be effectively studied with Mar... more Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the evolutionary behavior of the computer system by a continuous-time Markov chain, and a reward rate is associated with each state. In reliability/availability models, upstates have reward rate 1, and down states have reward rate zero associated with them. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Steady-state expected reward rate and expected instantaneous reward rate are clearly useful measures which can be extracted from the Markov reward model. The diversity of areas where Markov reward models may be used is illustrated with a comparative study of three examples of interest to the fault tolerant computing community.
Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, ... more Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, which use tools from the topology of real manifolds. Simpler proofs were discovered in the new century, of the Hilbert Nullstellensatz, and the Gelfand-Mazur Theorem. We give a related proof that an irreducible real polynomial has degree 2 or less, Gauss's form of the Fundamental Theorem of Algebra. It has been debated whether an elementary proof for FTA can be found, using the Brouwer Fixed-Point Theorem as its "analytical" component. In the present case the analytic or topological tool employed is Brouwer's Theorem on Invariance of Domain, which derives from his Fixed-Point Theorem. A corollary of Domain Invariance is that an injective mapping of one compact manifold to another (connected) one of the same dimension, is in fact surjective and a homeomorphism. The desired result (FTA) comes from the fact that a real sphere and its (quotient) projective space of the same...
An adolescent version of Lebesgue theory considers countable subsets of the real numbers. A funct... more An adolescent version of Lebesgue theory considers countable subsets of the real numbers. A function which is right-continuous "nearly always" (except for countably many) is also continuous nearly always. A function with either a right-hand or a left-hand derivative existing nearly always, is differentiable nearly always. This is a stronger result than presented in classical texts. To deal with a higher one-sided derivative, the Taylor "jet" approach is suggested, and hints are given for an Internal Set Theory generalization, replacing limits by arithmetic in non-Standard real numbers.
A closed-form formula for all the Fibonacci numbers, conjectured by the electrical engineer S.D. ... more A closed-form formula for all the Fibonacci numbers, conjectured by the electrical engineer S.D. Bedrosian, is described and proven by two distinct methods. The first method illustrates several principles of analysis and linear algebra, and is ideal for classroom explanation of an unexpected result that can be verified using calculators. The proof does not use complex numbers or algebraic equations, the Binet formula, generating functions, or resultant constructions. It does use the addition law of the sine and cosine, the relation between the set of eigenvalues (where these are simple and distinct) and the determinant,, and the Laplace expansion. The second proof was provided at one sitting by an anonymous geometer, and uses complex numbers, roots of unity, and the Binet formula,
The Maximum Principle from elliptic PDE has a simple constructive proof. This proof in fact leads... more The Maximum Principle from elliptic PDE has a simple constructive proof. This proof in fact leads to a factorization of any real polynomial whose degree is 3 or greater, the Fundamental Theorem of Algebra. The reciprocal polynomial function leads to two harmonic functions of two variables conjugate to each other and continuous everywhere. This leads to a contradiction with the Maximum Principle applied to a perturbed function. The technique is basically an analytic version of work of R. Redheffer from the 1950s, which gave more of a formal and combinatorial impression.
Proceedings of the 2012 ACM Research in Applied Computation Symposium on - RACS '12, 2012
The Polynomial method described in has been implemented for the non-singular rational square matr... more The Polynomial method described in has been implemented for the non-singular rational square matrix A for the computation of e At using the P-adic arithmetic software package---Exact Scientific Computational Library (ESCL) which we have developed. During the calculation process, truncation error is completely avoided. Efficiency comparisons have been investigated with direct summation, P-adic integer and P-adic long-integer data type representations .
International Journal of Networked and Distributed Computing, 2013
A P-adic Exact Scientific Computational Library (ESCL) for rational matrix operations has been de... more A P-adic Exact Scientific Computational Library (ESCL) for rational matrix operations has been developed over the past few years. The effort has been focusing on converting all rational number operations to integer calculation, and fully taking advantage of the fast integer multiplication of modern computer architectures. In this paper, we report our progress on parallel implementation of P-adic arithmetic by means of a multiple modulus rational system related to the Chinese remainder theorem. Experimental results are given to illustrate computational efficiency.
Hensel code was originally defined by Krishnamurthy, Rao and Subramanian [1], which was developed... more Hensel code was originally defined by Krishnamurthy, Rao and Subramanian [1], which was developed from the P-adic number system first proposed by Hensel in 1900s. The purpose was to realize exact computation for rational numbers. The Hensel code arithmetic has been well developed [1, 2, 3], but the problem of detecting Hensel code overflow and underflow has not been properly addressed . In this paper, we proposed a method for Hensel code overflow detection. The method can realize overflow detection by the prime p and the Hensel code itself. Using this method, a few digits of the Hensel code will be sacrificed.
ABSTRACT Automatic target recognition, or target discrimination, is an ever-increasing need in bo... more ABSTRACT Automatic target recognition, or target discrimination, is an ever-increasing need in both tactical and strategic engage-ments. Complex imaging systems, such as those based on adaptive optics compensation, are proven but expensive. This paper addresses a specific problem amenable to non-imaging distinction of targets, specifically symmetric and oblong. The approach is to illuminate a target with a rotating oblong beam, either in the near field (tactical) or far field (strate-gic). The returns from a symmetric object in the absence of pointing errors will be constant while returns from an oblong object will produce a sinusoidal signal, thus distinguishing the objects without imaging. This paper addresses the result of illumination with an oblong beam, starting with a pure beam, a beam corrupted by atmospheric effects and a beam affected by pointing errors referred to as jitter and boresight.
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Papers by Jon Sjogren