The minimal deterministic finite automaton is generally used to determine regular languages equal... more The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algorithm to non-deterministic finite automaton, and establish a relationship between this algorithm and the one proposed in Almeida et al. We also present some experimental comparative results. All these algorithms are closely related with the recent coalgebraic approach to automata proposed by Rutten. 1
In this work we propose an hybrid verification framework for hard real-time systems. The approach... more In this work we propose an hybrid verification framework for hard real-time systems. The approach is to use both static and dynamic verification techniques in the sense that dynamic verification is used to address the parts on which static verification fails or is very hard to obtain success. Towards the Specification and Verification Frameworks for Concurrent Real-Time Systems David Pereira, Andre Pedro, Luis Miguel Pinho, Jorge Sousa Pinto {dmrpe,anmap,lmp}@isep.ipp.pt, [email protected] • Concurrent real-time systems are growing dramatically, both in size and complexity • Verification, already challenging, is highly impacted from this growth • Integrated frameworks are fundamental to tackle all the intricacies of these systems • Formal languages that specify both timed and functional properties (at the source-level) • Regular expressions as formally verified models for lightweight and expressive runtime monitoring systems • Timed and hybrid logics as a high-level specification for...
Several methods have been proposed for performing schedulability analysis for both uni-processor ... more Several methods have been proposed for performing schedulability analysis for both uni-processor and multi-processor real-time systems. Very few of these works use the power of formal logic to write unambiguous specifications and to allow the usage of theorem provers for building the proofs of interest with greater correctness guarantees. In this paper we address this challenge by: 1) defining a formal language that allows to specify periodic resource models; 2) describe a transformational approach to reasoning about timing properties of resource models by transforming the latter specifications into a satisfiability modulo theories problem.
Several methods have been proposed for performingschedulability analysis for both uni-processor a... more Several methods have been proposed for performingschedulability analysis for both uni-processor and multiprocessorreal-time systems. Very few of these works use the power offormal logic to write unambiguous specifications and to allowthe usage of theorem provers for building the proofs of interestwith greater correctness guarantees. In this paper we addressthis challenge by: 1) defining a formal language that allows tospecify periodic resource models; 2) describe a transformationalapproach to reasoning about timing properties of resource modelsby transforming the latter specifications into a SMT problem. SMT-based Schedulability Analysis using RMTL- ABSTRACT Several methods have been proposed for performing schedulability analysis for both uni-processor and multi-processor real-time systems. Very few of these works use the power of formal logic to write unambiguous specifications and to allow the usage of theorem provers for building the proofs of interest with greater correctness g...
2020 International Symposium on Theoretical Aspects of Software Engineering (TASE), 2020
This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SA... more This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SAT solving modulo theories. RMTL-is a real-time version of metric temporal logic (MTL) extended by a duration quantifier allowing to measure time durations. For any given formula, a SAT instance modulo the theory of arrays, uninterpreted functions with equality and non-linear real-arithmetic is synthesized and may then be further investigated using appropriate SMT solvers. We show the benefits of using RMTL-with the given SMT encoding on a diversified set of examples that include in particular its application in the area of schedulability analysis. Therefore, we introduce a simple language for formalizing schedulability problems and show how to formulate timing constraints as RMTLformulas. Our practical evaluation based on our synthesis and Z3 as back-end SMT solver also shows the feasibility of the overall approach.
Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted ... more Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted fragment of MTL-R , we propose a new approach for the runtime verification of hard real-time systems. The novelty of our technique is that it is based on incremental evaluation, allowing us to e↵ectively treat duration properties (which play a crucial role in real-time systems). We describe the two levels of operation of our approach: o✏ine simplification by quantifier removal techniques; and online evaluation of a three-valued interpretation for formulas of our fragment. Our experiments show the applicability of this mechanism as well as the validity of the provided complexity results.
2020 International Symposium on Theoretical Aspects of Software Engineering (TASE), 2020
This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SA... more This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SAT solving modulo theories. RMTL-is a real-time version of metric temporal logic (MTL) extended by a duration quantifier allowing to measure time durations. For any given formula, a SAT instance modulo the theory of arrays, uninterpreted functions with equality and non-linear real-arithmetic is synthesized and may then be further investigated using appropriate SMT solvers. We show the benefits of using RMTL-with the given SMT encoding on a diversified set of examples that include in particular its application in the area of schedulability analysis. Therefore, we introduce a simple language for formalizing schedulability problems and show how to formulate timing constraints as RMTLformulas. Our practical evaluation based on our synthesis and Z3 as back-end SMT solver also shows the feasibility of the overall approach.
Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted ... more Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted fragment of MTL-R , we propose a new approach for the runtime verification of hard real-time systems. The novelty of our technique is that it is based on incremental evaluation, allowing us to e↵ectively treat duration properties (which play a crucial role in real-time systems). We describe the two levels of operation of our approach: o✏ine simplification by quantifier removal techniques; and online evaluation of a three-valued interpretation for formulas of our fragment. Our experiments show the applicability of this mechanism as well as the validity of the provided complexity results.
Over the past decades several approaches for schedulability analysis have been proposed for both ... more Over the past decades several approaches for schedulability analysis have been proposed for both uni-processor and multi-processor real-time systems. Although different techniques are employed, very little has been put forward in using formal specifications, with the consequent possibility for misinterpretations or ambiguities in the problem statement. Using a logic based approach to schedulability analysis in the design of hard real-time systems eases the synthesis of correct-by-construction procedures for both static and dynamic verification processes. In this paper we propose a novel approach to schedulability analysis based on a timed temporal logic with time durations. Our approach subsumes classical methods for uni-processor scheduling analysis over compositional resource models by providing the developer with counter-examples, and by ruling out schedules that cause unsafe violations on the system. We also provide an example showing the effectiveness of our proposal.
Runtime Monitoring of hard real-time embedded systems is a promising technique for ensuring that ... more Runtime Monitoring of hard real-time embedded systems is a promising technique for ensuring that a running system respects timing constraints, possibly combined with faults originated by the software and/or hardware. This is particularly important when we have real-time embedded systems made of several components that must combine different levels of criticality, and different levels of correctness requirements. This paper introduces a compositional monitoring framework coupled with guarantees that include time isolation and the response time of a monitor for a predicted violation. The kind of monitors that we propose are automatically generated by synthesizing logic formulas of a timed temporal logic, and their correctness is ensured by construction.
In this report we describe the formalisation of a simple imperative language with concurrent/para... more In this report we describe the formalisation of a simple imperative language with concurrent/parallel and atomic execution statements within the Coq theorem prover. Our formalisation includes the specification of a simple imperative programming language with statements for parallel and atomic execution of code, an underlying small-step structural semantics and a proof system that is sound with respect to such semantics. With this formalisation we give a first step towards the certified verification of sharedvariable concurrent/parallel programs under the context of Cliff Jones’ Rely-Guarantee reasoning and in the logic of Coq.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2011
In this paper we present a computer assisted proof of the correctness of a partial derivative aut... more In this paper we present a computer assisted proof of the correctness of a partial derivative automata construction from a regular expression within the Coq proof assistant. This proof is part of a formalization of Kleene algebra and regular languages in Coq towards their usage in program certification.
Kleene algebra [1],(KA) normally called the algebra of regular events, is an algebraic system tha... more Kleene algebra [1],(KA) normally called the algebra of regular events, is an algebraic system that axiomatically captures properties of several important structures arising in Computer Science, and has been applied in several contexts like automata and formal languages, semantics and logic of programs, design and analysis of algorithms, among others. Kleene algebra with tests (KAT)[2] extends KA with an embedded Boolean algebra and is particularly suited for the formal verification of propositional programs. In ...
The BDI model of agency is a well studied concept in Formal Logic for Rational Agents, mainly thr... more The BDI model of agency is a well studied concept in Formal Logic for Rational Agents, mainly through the BDICTL [7] and KARO [7] logical frameworks. The former is based on the Branching Time Logic CTL [3], whereas the latter in based on Dynamic Logic [4]. Both have advantages and disadvantages, but the union of some properties of both frameworks provide, in our opinion, all the formal tools that we need to model the more recently introduced concept of Artificial Emotion within the BDI model [2]. In this work we ...
Kleene algebra (KA) is an algebraic system that captures properties of several important structur... more Kleene algebra (KA) is an algebraic system that captures properties of several important structures arising in Computer Science like automata and formal languages, among others. In this paper we present a formalization of regular languages as a KA in the Coq theorem prover. In particular, we describe the implementation of an algorithm for deciding regular expressions equivalence based on the notion of derivative. We envision the usage of (an extension of) our formalization as the formal system in which we can ...
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012
In this paper we present a mechanically verified implementation of an algorithm for deciding regu... more In this paper we present a mechanically verified implementation of an algorithm for deciding regular expression (in-)equivalence within the Coq proof assistant. This algorithm is a version of a functional algorithm proposed by Almeida et al. which decides regular expression equivalence through an iterated process of testing the equivalence of their partial derivatives. In particular, this algorithm has a refutation step which improves the process of checking if two regular expressions are not equivalent.
Para os meus pais David e Maria Clara e para a Ana... v vi I am particularly indebted to José Car... more Para os meus pais David e Maria Clara e para a Ana... v vi I am particularly indebted to José Carlos Bacelar Almeida who was always available to discuss with me several technical issues related to Coq. I also thank Ricardo Almeida for our discussions about Kleene algebra with tests. To Rogério Reis, my sincere thanks for being such a good teacher.
Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted ... more Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted fragment of MTLD, we propose a new approach for the runtime verification of hard real-time systems. The novelty of our technique is that it is based on incremental evaluation, allowing us to effectively treat duration properties (which play a crucial role in real-time systems). We describe the two levels of operation of our approach: offline simplification by quantifier removal techniques; and online evaluation of a three-valued interpretation for formulas of our fragment. Our experiments show the applicability of this mechanism as well as the validity of the provided complexity results. Monitoring for a decidable fragment of MTL∫ André de Matos Pedro, David Pereira, Lúıs Miguel Pinho, and Jorge Sousa Pinto 1 CISTER/INESC TEC, ISEP, Polytechnic Institute of Porto, Portugal 2 HASLab/INESC TEC & Universidade do Minho, Portugal Abstract. Temporal logics targeting real-time systems are tradi...
Abstract. Emotional-BDI agents are agents whose behaviour is guided not only by beliefs, desires ... more Abstract. Emotional-BDI agents are agents whose behaviour is guided not only by beliefs, desires and intentions, but also by the role of emotions in reasoning and decision-making. In this paper we introduce the logic EBDI for specifying Emotional-BDI agents in general and a special kind of Emotional-BDI agent under the effect of fear. The focus of this work is in the expressiveness of EBDI and on using it to establish some properties which agents under the effect of an emotion should exhibit. 1
Journal of Logical and Algebraic Methods in Programming, 2014
This paper presents a mechanically verified implementation of an algorithm for deciding the equiv... more This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based in automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.
The minimal deterministic finite automaton is generally used to determine regular languages equal... more The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algorithm to non-deterministic finite automaton, and establish a relationship between this algorithm and the one proposed in Almeida et al. We also present some experimental comparative results. All these algorithms are closely related with the recent coalgebraic approach to automata proposed by Rutten. 1
In this work we propose an hybrid verification framework for hard real-time systems. The approach... more In this work we propose an hybrid verification framework for hard real-time systems. The approach is to use both static and dynamic verification techniques in the sense that dynamic verification is used to address the parts on which static verification fails or is very hard to obtain success. Towards the Specification and Verification Frameworks for Concurrent Real-Time Systems David Pereira, Andre Pedro, Luis Miguel Pinho, Jorge Sousa Pinto {dmrpe,anmap,lmp}@isep.ipp.pt, [email protected] • Concurrent real-time systems are growing dramatically, both in size and complexity • Verification, already challenging, is highly impacted from this growth • Integrated frameworks are fundamental to tackle all the intricacies of these systems • Formal languages that specify both timed and functional properties (at the source-level) • Regular expressions as formally verified models for lightweight and expressive runtime monitoring systems • Timed and hybrid logics as a high-level specification for...
Several methods have been proposed for performing schedulability analysis for both uni-processor ... more Several methods have been proposed for performing schedulability analysis for both uni-processor and multi-processor real-time systems. Very few of these works use the power of formal logic to write unambiguous specifications and to allow the usage of theorem provers for building the proofs of interest with greater correctness guarantees. In this paper we address this challenge by: 1) defining a formal language that allows to specify periodic resource models; 2) describe a transformational approach to reasoning about timing properties of resource models by transforming the latter specifications into a satisfiability modulo theories problem.
Several methods have been proposed for performingschedulability analysis for both uni-processor a... more Several methods have been proposed for performingschedulability analysis for both uni-processor and multiprocessorreal-time systems. Very few of these works use the power offormal logic to write unambiguous specifications and to allowthe usage of theorem provers for building the proofs of interestwith greater correctness guarantees. In this paper we addressthis challenge by: 1) defining a formal language that allows tospecify periodic resource models; 2) describe a transformationalapproach to reasoning about timing properties of resource modelsby transforming the latter specifications into a SMT problem. SMT-based Schedulability Analysis using RMTL- ABSTRACT Several methods have been proposed for performing schedulability analysis for both uni-processor and multi-processor real-time systems. Very few of these works use the power of formal logic to write unambiguous specifications and to allow the usage of theorem provers for building the proofs of interest with greater correctness g...
2020 International Symposium on Theoretical Aspects of Software Engineering (TASE), 2020
This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SA... more This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SAT solving modulo theories. RMTL-is a real-time version of metric temporal logic (MTL) extended by a duration quantifier allowing to measure time durations. For any given formula, a SAT instance modulo the theory of arrays, uninterpreted functions with equality and non-linear real-arithmetic is synthesized and may then be further investigated using appropriate SMT solvers. We show the benefits of using RMTL-with the given SMT encoding on a diversified set of examples that include in particular its application in the area of schedulability analysis. Therefore, we introduce a simple language for formalizing schedulability problems and show how to formulate timing constraints as RMTLformulas. Our practical evaluation based on our synthesis and Z3 as back-end SMT solver also shows the feasibility of the overall approach.
Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted ... more Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted fragment of MTL-R , we propose a new approach for the runtime verification of hard real-time systems. The novelty of our technique is that it is based on incremental evaluation, allowing us to e↵ectively treat duration properties (which play a crucial role in real-time systems). We describe the two levels of operation of our approach: o✏ine simplification by quantifier removal techniques; and online evaluation of a three-valued interpretation for formulas of our fragment. Our experiments show the applicability of this mechanism as well as the validity of the provided complexity results.
2020 International Symposium on Theoretical Aspects of Software Engineering (TASE), 2020
This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SA... more This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SAT solving modulo theories. RMTL-is a real-time version of metric temporal logic (MTL) extended by a duration quantifier allowing to measure time durations. For any given formula, a SAT instance modulo the theory of arrays, uninterpreted functions with equality and non-linear real-arithmetic is synthesized and may then be further investigated using appropriate SMT solvers. We show the benefits of using RMTL-with the given SMT encoding on a diversified set of examples that include in particular its application in the area of schedulability analysis. Therefore, we introduce a simple language for formalizing schedulability problems and show how to formulate timing constraints as RMTLformulas. Our practical evaluation based on our synthesis and Z3 as back-end SMT solver also shows the feasibility of the overall approach.
Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted ... more Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted fragment of MTL-R , we propose a new approach for the runtime verification of hard real-time systems. The novelty of our technique is that it is based on incremental evaluation, allowing us to e↵ectively treat duration properties (which play a crucial role in real-time systems). We describe the two levels of operation of our approach: o✏ine simplification by quantifier removal techniques; and online evaluation of a three-valued interpretation for formulas of our fragment. Our experiments show the applicability of this mechanism as well as the validity of the provided complexity results.
Over the past decades several approaches for schedulability analysis have been proposed for both ... more Over the past decades several approaches for schedulability analysis have been proposed for both uni-processor and multi-processor real-time systems. Although different techniques are employed, very little has been put forward in using formal specifications, with the consequent possibility for misinterpretations or ambiguities in the problem statement. Using a logic based approach to schedulability analysis in the design of hard real-time systems eases the synthesis of correct-by-construction procedures for both static and dynamic verification processes. In this paper we propose a novel approach to schedulability analysis based on a timed temporal logic with time durations. Our approach subsumes classical methods for uni-processor scheduling analysis over compositional resource models by providing the developer with counter-examples, and by ruling out schedules that cause unsafe violations on the system. We also provide an example showing the effectiveness of our proposal.
Runtime Monitoring of hard real-time embedded systems is a promising technique for ensuring that ... more Runtime Monitoring of hard real-time embedded systems is a promising technique for ensuring that a running system respects timing constraints, possibly combined with faults originated by the software and/or hardware. This is particularly important when we have real-time embedded systems made of several components that must combine different levels of criticality, and different levels of correctness requirements. This paper introduces a compositional monitoring framework coupled with guarantees that include time isolation and the response time of a monitor for a predicted violation. The kind of monitors that we propose are automatically generated by synthesizing logic formulas of a timed temporal logic, and their correctness is ensured by construction.
In this report we describe the formalisation of a simple imperative language with concurrent/para... more In this report we describe the formalisation of a simple imperative language with concurrent/parallel and atomic execution statements within the Coq theorem prover. Our formalisation includes the specification of a simple imperative programming language with statements for parallel and atomic execution of code, an underlying small-step structural semantics and a proof system that is sound with respect to such semantics. With this formalisation we give a first step towards the certified verification of sharedvariable concurrent/parallel programs under the context of Cliff Jones’ Rely-Guarantee reasoning and in the logic of Coq.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2011
In this paper we present a computer assisted proof of the correctness of a partial derivative aut... more In this paper we present a computer assisted proof of the correctness of a partial derivative automata construction from a regular expression within the Coq proof assistant. This proof is part of a formalization of Kleene algebra and regular languages in Coq towards their usage in program certification.
Kleene algebra [1],(KA) normally called the algebra of regular events, is an algebraic system tha... more Kleene algebra [1],(KA) normally called the algebra of regular events, is an algebraic system that axiomatically captures properties of several important structures arising in Computer Science, and has been applied in several contexts like automata and formal languages, semantics and logic of programs, design and analysis of algorithms, among others. Kleene algebra with tests (KAT)[2] extends KA with an embedded Boolean algebra and is particularly suited for the formal verification of propositional programs. In ...
The BDI model of agency is a well studied concept in Formal Logic for Rational Agents, mainly thr... more The BDI model of agency is a well studied concept in Formal Logic for Rational Agents, mainly through the BDICTL [7] and KARO [7] logical frameworks. The former is based on the Branching Time Logic CTL [3], whereas the latter in based on Dynamic Logic [4]. Both have advantages and disadvantages, but the union of some properties of both frameworks provide, in our opinion, all the formal tools that we need to model the more recently introduced concept of Artificial Emotion within the BDI model [2]. In this work we ...
Kleene algebra (KA) is an algebraic system that captures properties of several important structur... more Kleene algebra (KA) is an algebraic system that captures properties of several important structures arising in Computer Science like automata and formal languages, among others. In this paper we present a formalization of regular languages as a KA in the Coq theorem prover. In particular, we describe the implementation of an algorithm for deciding regular expressions equivalence based on the notion of derivative. We envision the usage of (an extension of) our formalization as the formal system in which we can ...
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012
In this paper we present a mechanically verified implementation of an algorithm for deciding regu... more In this paper we present a mechanically verified implementation of an algorithm for deciding regular expression (in-)equivalence within the Coq proof assistant. This algorithm is a version of a functional algorithm proposed by Almeida et al. which decides regular expression equivalence through an iterated process of testing the equivalence of their partial derivatives. In particular, this algorithm has a refutation step which improves the process of checking if two regular expressions are not equivalent.
Para os meus pais David e Maria Clara e para a Ana... v vi I am particularly indebted to José Car... more Para os meus pais David e Maria Clara e para a Ana... v vi I am particularly indebted to José Carlos Bacelar Almeida who was always available to discuss with me several technical issues related to Coq. I also thank Ricardo Almeida for our discussions about Kleene algebra with tests. To Rogério Reis, my sincere thanks for being such a good teacher.
Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted ... more Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted fragment of MTLD, we propose a new approach for the runtime verification of hard real-time systems. The novelty of our technique is that it is based on incremental evaluation, allowing us to effectively treat duration properties (which play a crucial role in real-time systems). We describe the two levels of operation of our approach: offline simplification by quantifier removal techniques; and online evaluation of a three-valued interpretation for formulas of our fragment. Our experiments show the applicability of this mechanism as well as the validity of the provided complexity results. Monitoring for a decidable fragment of MTL∫ André de Matos Pedro, David Pereira, Lúıs Miguel Pinho, and Jorge Sousa Pinto 1 CISTER/INESC TEC, ISEP, Polytechnic Institute of Porto, Portugal 2 HASLab/INESC TEC & Universidade do Minho, Portugal Abstract. Temporal logics targeting real-time systems are tradi...
Abstract. Emotional-BDI agents are agents whose behaviour is guided not only by beliefs, desires ... more Abstract. Emotional-BDI agents are agents whose behaviour is guided not only by beliefs, desires and intentions, but also by the role of emotions in reasoning and decision-making. In this paper we introduce the logic EBDI for specifying Emotional-BDI agents in general and a special kind of Emotional-BDI agent under the effect of fear. The focus of this work is in the expressiveness of EBDI and on using it to establish some properties which agents under the effect of an emotion should exhibit. 1
Journal of Logical and Algebraic Methods in Programming, 2014
This paper presents a mechanically verified implementation of an algorithm for deciding the equiv... more This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based in automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.
Uploads
Papers by David Pereira