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Sequent Calculi for Process Verification: HennessyMilner Logic for an Arbitrary GSOS
, 2003
"... We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satis ..."
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Cited by 11 (1 self)
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We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satisfy assertions in HennessyMilner logic. The main novelty lies in the use of the operational semantics to derive introduction rules, on the left and right of sequents, for the operators of the process calculus. This gives a generic proof system applicable to any process algebra with an operational semantics specified in the GSOS format. Using a general algebraic notion of GSOS model, we prove a completeness theorem for the cutfree fragment of the proof system, thereby establishing the admissibility of the cut rule. Under mild (and necessary) conditions on the process algebra, an ωcompleteness result, relative to the “intended” model of closed process terms, follows.
Compositionality of HennessyMilner logic through structural operational semantics
 Huang and M. E. Glicksman, Acta Met
, 2003
"... Abstract. This paper presents a method for the decomposition of HML formulae. It can be used to decide whether a process algebra term satisfies a HML formula, by checking whether subterms satisfy certain formulae, obtained by decomposing the original formula. The method uses the structural operation ..."
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Cited by 8 (1 self)
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Abstract. This paper presents a method for the decomposition of HML formulae. It can be used to decide whether a process algebra term satisfies a HML formula, by checking whether subterms satisfy certain formulae, obtained by decomposing the original formula. The method uses the structural operational semantics of the process algebra. The main contribution of this paper is that an earlier decomposition method from Larsen [14] for the De Simone format is extended to the more general ntyft/ntyxt format without lookahead. 1
Bialgebraic Methods and Modal Logic in Structural Operational Semantics
 Electronic Notes in Theoretical Computer Science
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various ..."
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Cited by 8 (3 self)
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOSlike specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1
Proving ∀µcalculus properties with satbased model checking
 Volume 3731 of LNCS., SpringerVerlag
, 2005
"... Abstract. In this paper, we present a complete bounded model checking algorithm for the universal fragment of µcalculus. The new algorithm checks the completeness of bounded proof of each property on the fly and does not depend on prior knowledge of the completeness thresholds. The key is to combin ..."
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Cited by 2 (1 self)
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Abstract. In this paper, we present a complete bounded model checking algorithm for the universal fragment of µcalculus. The new algorithm checks the completeness of bounded proof of each property on the fly and does not depend on prior knowledge of the completeness thresholds. The key is to combine both local and bounded model checking techniques and use SAT solvers to perform local model checking on finite Kripke structures. Our prooftheoretic approach works for any property in the specification logic and is more general than previous work on specific properties. We report experimental results to compare our algorithm with the conventional BDDbased algorithm. 1
The Power of Parameterization in Coinductive Proof
"... Coinduction is one of the most basic concepts in computer science. It is therefore surprising that the commonlyknown latticetheoretic accounts of the principles underlying coinductive proofs are lacking in two key respects: they do not support compositional reasoning (i.e., breaking proofs into se ..."
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Cited by 1 (1 self)
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Coinduction is one of the most basic concepts in computer science. It is therefore surprising that the commonlyknown latticetheoretic accounts of the principles underlying coinductive proofs are lacking in two key respects: they do not support compositional reasoning (i.e., breaking proofs into separate pieces that can be developed in isolation), and they do not support incremental reasoning (i.e., developing proofs interactively by starting from the goal and generalizing the coinduction hypothesis repeatedly as necessary). In this paper, we show how to support coinductive proofs that are both compositional and incremental, using a dead simple construction we call the parameterized greatest fixed point. The basic idea is to parameterize the greatest fixed point of interest over the accumulated knowledge of “the proof so far”. While this idea has been proposed before, by Winskel in 1989 and by Moss in 2001, neither of the previous accounts suggests its general applicability to improving the state of the art in interactive coinductive proof. In addition to presenting the latticetheoretic foundations of parameterized coinduction, demonstrating its utility on representative examples, and studying its composition with “upto ” techniques, we also explore its mechanization in proof assistants like Coq and Isabelle. Unlike traditional approaches to mechanizing coinduction (e.g., Coq’s cofix), which employ syntactic “guardedness checking”, parameterized coinduction offers a semantic account of guardedness. This leads to faster and more robust proof development, as we demonstrate using our new Coq library, Paco.
Modal µTypes for Processes
, 1995
"... We introduce a new paradigm for concurrency, called behavioursastypes. In this paradigm, types are used to convey information about the behaviour of processes: while terms corresponds to processes, types correspond to behaviours. We apply this paradigm to Winskel's Process Algebra. Its types are ..."
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We introduce a new paradigm for concurrency, called behavioursastypes. In this paradigm, types are used to convey information about the behaviour of processes: while terms corresponds to processes, types correspond to behaviours. We apply this paradigm to Winskel's Process Algebra. Its types are similar to Kozen's modal calculus; hence, they are called modal types. We prove that two terms having the same type denote two processes which behave in the same way, that is, they are bisimilar. We give a sound and complete compositional typing system for this language. Such a system naturally recovers the notion of bisimulation also on open terms, allowing us to deal with processes with undefined parts in a compositional manner. 1
Bialgebraic Operational Semantics and Modal Logic (extended abstract)
"... A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by Structural Operational Semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived fr ..."
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A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by Structural Operational Semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived from the corresponding sets for its subprocesses, then the logical equivalence is a congruence. Striving for generality, SOS rules are modeled categorically as bialgebraic distributive laws for some notions of process syntax and behaviour, and modal logics are modeled via coalgebraic polyadic modal logic. Compositionality is proved by providing a suitable notion of behaviour for the logic together with a dual distributive law, reflecting the one modeling the SOS specification. Concretely, the dual laws may appear as SOSlike rules where logical formulas play the role of processes, and their behaviour models logical decomposition over process syntax. The approach can be used either to proving compositionality for specific languages or for defining SOS congruence formats.
Data Structures of Bounded Degree with Constant Update Time
, 1994
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS