Luis Fernando Pino

Deriving labels and bisimilarity for concurrent constraint programming

Concurrent constraint programming (ccp) is a well-established model for concurrency. Bisimilarity is one of the central reasoning techniques in concurrency. The standard definition of bisimilarity, however, is not completely satisfactory for ccp since it yields an equivalence that is too fine grained. By building upon recent foundational investigations, we introduce a labelled transition semantics and a novel notion of bisimilarity that is fully abstract w.r.t. the typical observational equivalence in ccp.

Partition refinement for bisimilarity in CCP

Saraswats concurrent constraint programming (ccp) is a mature formalism for modeling processes (or programs) that interact by telling and asking constraints in a global medium, called the store. Bisimilarity is a standard behavioural equivalence in concurrency theory, but a well-behaved notion of bisimilarity for ccp has been proposed only recently. When the state space of a system is finite, the ordinary notion of bisimilarity can be computed via the well-known partition refinement algorithm, but unfortunately, this algorithm does not work for ccp bisimilarity. In this paper, we propose a variation of the partition refinement algorithm for verifying ccp bisimilarity. To the best of our knowledge this is the first work providing for the automatic verification of program equivalence for ccp.

Reducing Weak to Strong Bisimilarity in CCP

Concurrent constraint programming (ccp) is a well-established model for concurrency that singles out the fundamental aspects of asynchronous systems whose agents (or processes) evolve by posting and querying (partial) information in a global medium. Bisimilarity is a standard behavioural equivalence in concurrency theory. However, only recently a well-behaved notion of bisimilarity for ccp, and a ccp partition refinement algorithm for deciding the strong version of this equivalence have been proposed. Weak bisimiliarity is a central behavioural equivalence in process calculi and it is obtained from the strong case by taking into account only the actions that are observable in the system. Typically, the standard partition refinement can also be used for deciding weak bisimilarity simply by using Milners reduction from weak to strong bisimilarity; a technique referred to as saturation. In this paper we demonstrate that, because of its involved labeled transitions, the above-mentioned saturation technique does not work for ccp. We give an alternative reduction from weak ccp bisimilarity to the strong one that allows us to use the ccp partition refinement algorithm for deciding this equivalence.

A Labelled Semantics for Soft Concurrent Constraint Programming

We present a labelled semantics for Soft Concurrent Constraint Programming (SCCP), a language where concurrent agents may synchronize on a shared store by either posting or checking the satisfaction of (soft) constraints. SCCP generalizes the classical formalism by parametrising the constraint system over an order-enriched monoid: the monoid operator is not required to be idempotent, thus adding the same information several times may change the store. The novel operational rules are shown to offer a sound and complete co-inductive technique to prove the original equivalence over the unlabelled semantics.

A Behavioral Congruence for Concurrent Constraint Programming with Nondeterministic Choice

Concurrent constraint programming (ccp) is a well-established model of concurrency for reasoning about systems of multiple agents that interact with each other by posting and querying partial information on a shared space. (Weak) bisimilarity is one of the most representative notions of behavioral equivalence for models of concurrency. A notion of weak bisimilarity, called weak saturated bisimilarity (\(\dot{\approx}_{sb}\)), was recently proposed for ccp. This equivalence improves on previous bisimilarity notions for ccp that were too discriminating and it is a congruence for the choice-free fragment of ccp. In this paper, however, we show that \(\dot{\approx}_{sb}\) is not a congruence for ccp with nondeterministic choice. We then introduce a new notion of bisimilarity, called weak full bisimilarity (≈ f ), and show that it is a congruence for the full language of ccp. We also show the adequacy of ≈ f by establishing that it coincides with the congruence induced by closing \(\dot{\approx}_{sb}\) under all contexts. The advantage of the new definition is that, unlike the congruence induced by \(\dot{\approx}_{sb}\), it does not require quantifying over infinitely many contexts.

Efficient computation of 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 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.

Observational and behavioural equivalences for soft concurrent constraint programming

We present a labelled semantics for Soft Concurrent Constraint Programming (SCCP), a meta-language where concurrent agents may synchronise on a shared store by either posting or checking the satisfaction of (soft) constraints. SCCP generalises the classical formalism by parametrising the constraint system over an order-enriched monoid, thus abstractly representing the store with an element of the monoid, and the standard unlabelled semantics just observes store updates. The novel operational rules are shown to offer a sound and complete co-inductive technique to prove the original equivalence over the unlabelled semantics. Based on this characterisation, we provide an axiomatisation for finite agents.

Weak CCP bisimilarity with strong procedures

We show that the standard saturation method for reducing weak bisimilarity to strong bisimilarity does not work for CCP.We provide a new saturation method for reducing weak bisimilarity to strong bisimilarity for CCP.We prove that due to distinctive nature of CCP, the new method does not introduce infinitely-branching in the resulting transition systems.We then derive an algorithm to automatically verify the notion of weak bisimilarity in CCP. Concurrent constraint programming (CCP) is a well-established model for concurrency that singles out the fundamental aspects of asynchronous systems whose agents (or processes) evolve by posting and querying (partial) information in a global medium. Bisimilarity is a standard behavioral equivalence in concurrency theory. However, only recently a well-behaved notion of bisimilarity for CCP, and a CCP partition refinement algorithm for deciding the strong version of this equivalence have been proposed. Weak bisimilarity is a central behavioral equivalence in process calculi and it is obtained from the strong case by taking into account only the actions that are observable in the system. Typically, the standard partition refinement can also be used for deciding weak bisimilarity simply by using Milners reduction from weak to strong bisimilarity; a technique referred to as saturation. In this paper we demonstrate that, because of its involved labeled transitions, the above-mentioned saturation technique does not work for CCP. We give an alternative reduction from weak CCP bisimilarity to the strong one that allows us to use the CCP partition refinement algorithm for deciding this equivalence.

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 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 CCPs program equivalence.