890 research outputs found

    Deciding observational congruence of finite-state CCS expressions by rewriting

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    AbstractWe propose a term rewriting approach to verify observational congruence between guarded recursive (finite-state) CCS expressions. Starting from the complete axiomatization of observational congruence for this subset of CCS, a non-terminating rewriting relation has been defined. This rewriting relation is ω-canonical over a subclass of infinite derivations, structured fair derivations, which compute all the ω-normal forms. The rewriting relation is shown to be complete with respect to the axiomatization by proving that every structured fair derivation computes a term that denotes an rτ-normal process graph. The existence of a finite representation for ω-normal forms allows the definition of a rewriting strategy that, in a finite number of rewriting steps, decides observational congruence of guarded recursive (finite-state) CCS expressions

    Proof techniques for CCS

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    Proofs of observational equivalence of behaviour expressions in Milner's Calculus of Communicating Systems can be quite lengthy, and as larger and more practical systems of agents are considered the need for shorter proof techniques becomes more important. In this thesis a number of results about the calculus are proved which give rise to give more natural techniques. Three principal areas of research are presented:(i) A study of strong confluence and determinacy is made, extending Hilner's work to the whole calculus - the appropriate modifications to take value-passing into account are motivated and defined, and a strong confluence theorem is proved. It is shown that a useful subcalculus of CCS is strongly confluent.(ii) An investigation into criteria for uniqueness of solution of equations pf the form b = Fib] is performed. To do this a concept of derivations of an agent A "causing" derivations of FlAl is defined; using this, conditions are imposed on F which imply uniqueness, and a study follows of how these conditions relate to the structure of F.(iii) By using an alternative, stronger, definition of observational equivalence as a maximal fixed point it is found that equivalences can be demonstrated by constructing bisimulations between agents, and results leading to an algorithm for such constructions are presented. Also, using this alternative definition a weaker form of confluence can be defined very easily, and this is investigated.The theoretical material in this thesis is supplemented by examples demonstrating how the results proved can be applied to give proof techniques for use within the calculus

    Dynamic Congruence vs. Progressing Bisimulation for CCS

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    Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g. \alpha.\tau.\beta.nil and \alpha.\beta.nil are woc but \tau.\beta.nil and \beta.nil are not. This fact prevent us from characterizing CCS semantics (when \tau is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e. run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two logical characterizations via modal logic in the style of HML and a complete axiomatization for finite agents (consisting of the axioms for Strong Observational Congruence and of two of the three Milner's Ï„\tau-laws). Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents

    Domain Theory for Concurrency

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    A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of linearity in concurrent computation. Two choices of comonad yield two expressive metalanguages for higher-order processes, both arising from canonical constructions in the model. Their denotational semantics are fully abstract with respect to contextual equivalence. One language derives from an exponential of linear logic; it supports a straightforward operational semantics with simple proofs of soundness and adequacy. The other choice of comonad yields a model of affine-linear logic, and a process language with a tensor operation to be understood as a parallel composition of independent processes. The domain theory can be generalised to presheaf models, providing a more refined treatment of nondeterministic branching. The article concludes with a discussion of a broader programme of research, towards a fully fledged domain theory for concurrency

    A New Linear Logic for Deadlock-Free Session-Typed Processes

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    The π -calculus, viewed as a core concurrent programming language, has been used as the target of much research on type systems for concurrency. In this paper we propose a new type system for deadlock-free session-typed π -calculus processes, by integrating two separate lines of work. The first is the propositions-as-types approach by Caires and Pfenning, which provides a linear logic foundation for session types and guarantees deadlock-freedom by forbidding cyclic process connections. The second is Kobayashi’s approach in which types are annotated with priorities so that the type system can check whether or not processes contain genuine cyclic dependencies between communication operations. We combine these two techniques for the first time, and define a new and more expressive variant of classical linear logic with a proof assignment that gives a session type system with Kobayashi-style priorities. This can be seen in three ways: (i) as a new linear logic in which cyclic structures can be derived and a CYCLE -elimination theorem generalises CUT -elimination; (ii) as a logically-based session type system, which is more expressive than Caires and Pfenning’s; (iii) as a logical foundation for Kobayashi’s system, bringing it into the sphere of the propositions-as-types paradigm

    Nominal Abstraction

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    Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and an encoding of binding constructs via generic judgments. However, logics encompassing these two features do not currently allow for the definition of relations that embody dynamic aspects related to binding, a capability needed in many reasoning tasks. We propose a new relation between terms called nominal abstraction as a means for overcoming this deficiency. We incorporate nominal abstraction into a rich logic also including definitions, generic quantification, induction, and co-induction that we then prove to be consistent. We present examples to show that this logic can provide elegant treatments of binding contexts that appear in many proofs, such as those establishing properties of typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.Comment: To appear in the Journal of Information and Computatio
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