Efficient algorithms for program equivalence for confluent concurrent constraint programming
Concurrent Constraint Programming (CCP) is a well-established declarative framework from concurrency theory. Its foundations and principles e.g., semantics, proof systems, axiomatizations, have been thoroughly studied for over the last two decades. In contrast, the development of algorithms and auto...
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| Vydané v: | Science of computer programming Ročník 111; s. 135 - 155 |
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| Jazyk: | English |
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Elsevier B.V
01.11.2015
Elsevier |
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| Abstract | Concurrent Constraint Programming (CCP) is a well-established declarative framework from concurrency theory. Its foundations and principles e.g., semantics, proof systems, axiomatizations, have been thoroughly studied for over the last two decades. In contrast, the development of algorithms and automatic verification procedures for CCP have hitherto been far too little considered. To the best of our knowledge there is only one existing verification algorithm for the standard notion of CCP program (observational) equivalence. In this paper we first show that this verification algorithm has an exponential-time complexity even for programs from a representative sub-language of CCP; the summation-free fragment ( CCP\+). We then significantly improve on the complexity of this algorithm by providing two alternative polynomial-time decision procedures for CCP\+ program equivalence. Each of these two procedures has an advantage over the other. One has a better time complexity. The other can be easily adapted for the full language of CCP to produce significant state space reductions. The relevance of both procedures derives from the importance of CCP\+. This fragment, which has been the subject of many theoretical studies, has strong ties to first-order logic and an elegant denotational semantics, and it can be used to model real-world situations. Its most distinctive feature is that of confluence, a property we exploit to obtain our polynomial procedures. Finally, we also study the congruence issues regarding CCP's program equivalence. |
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| AbstractList | Concurrent Constraint Programming (CCP) is a well-established declarative frame-work from concurrency theory. Its foundations and principles e.g., semantics, proof systems, axiomatizations, have been thoroughly studied for over the last two decades. In contrast, the development of algorithms and automatic verifica-tion procedures for CCP have hitherto been far too little considered. To the best of our knowledge there is only one existing verification algorithm for the standard notion of CCP program (observational) equivalence. In this paper we first show that this verification algorithm has an exponential-time complexity even for pro-grams from a representative sub-language of CCP; the summation-free fragment (CCP\+). We then significantly improve on the complexity of this algorithm by providing two alternative polynomial-time decision procedures for CCP\+ pro-gram equivalence. Each of these two procedures has an advantage over the other. One has a better time complexity. The other can be easily adapted for the full Concurrent Constraint Programming (CCP) is a well-established declarative framework from concurrency theory. Its foundations and principles e.g., semantics, proof systems, axiomatizations, have been thoroughly studied for over the last two decades. In contrast, the development of algorithms and automatic verification procedures for CCP have hitherto been far too little considered. To the best of our knowledge there is only one existing verification algorithm for the standard notion of CCP program (observational) equivalence. In this paper we first show that this verification algorithm has an exponential-time complexity even for programs from a representative sub-language of CCP; the summation-free fragment ( CCP\+). We then significantly improve on the complexity of this algorithm by providing two alternative polynomial-time decision procedures for CCP\+ program equivalence. Each of these two procedures has an advantage over the other. One has a better time complexity. The other can be easily adapted for the full language of CCP to produce significant state space reductions. The relevance of both procedures derives from the importance of CCP\+. This fragment, which has been the subject of many theoretical studies, has strong ties to first-order logic and an elegant denotational semantics, and it can be used to model real-world situations. Its most distinctive feature is that of confluence, a property we exploit to obtain our polynomial procedures. Finally, we also study the congruence issues regarding CCP's program equivalence. |
| Author | Bonchi, Filippo Valencia, Frank Pino, Luis F. |
| Author_xml | – sequence: 1 givenname: Luis F. surname: Pino fullname: Pino, Luis F. email: luis.pino@lix.polytechnique.fr organization: INRIA/DGA and LIX (UMR 7161 X-CNRS), École Polytechnique, 91128 Palaiseau Cedex, France – sequence: 2 givenname: Filippo surname: Bonchi fullname: Bonchi, Filippo email: filippo.bonchi@ens-lyon.fr organization: ENS Lyon, Université de Lyon, LIP (UMR 5668 CNRS ENS Lyon UCBL INRIA), 46 Allée d'Italie, 69364 Lyon, France – sequence: 3 givenname: Frank surname: Valencia fullname: Valencia, Frank email: frank.valencia@lix.polytechnique.fr organization: CNRS and LIX (UMR 7161 X-CNRS), École Polytechnique, 91128 Palaiseau Cedex, France |
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| Keywords | Concurrent constraint programming Observational equivalence Bisimulation Partition refinement |
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| SubjectTerms | Bisimulation Computer Science Concurrent constraint programming Formal Languages and Automata Theory Logic in Computer Science Observational equivalence Partition refinement |
| Title | Efficient algorithms for program equivalence for confluent concurrent constraint programming |
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