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18
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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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.
Partially Persistent Data Structures of Bounded Degree with Constant Update Time
 NORDIC JOURNAL OF COMPUTING
, 1996
"... The problem of making bounded indegree and outdegree data structures partially persistent is considered. The node copying method of Driscoll et al. is extended so that updates can be performed in worstcase constant time on the pointer machine model. Previously it was only known to be possible in ..."
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Cited by 14 (3 self)
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The problem of making bounded indegree and outdegree data structures partially persistent is considered. The node copying method of Driscoll et al. is extended so that updates can be performed in worstcase constant time on the pointer machine model. Previously it was only known to be possible in amortised constant time [2]. The result is presented in terms of a new strategy for Dietz and Raman's dynamic two player pebble game on graphs. It is shown how to implement the strategy and the upper bound on the required number of pebbles is improved from 2b+2d+O( p b) to d+2b, where b is the bound of the indegree and d the bound of the outdegree. We also give a lower bound that shows that the number of pebbles depends on the outdegree d.
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 14 (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
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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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.
On the proof theory of modal mucalculus
 Studia Logica
, 2008
"... We study the prooftheoretic relationship between two deductive systems for the modal mucalculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a ..."
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We study the prooftheoretic relationship between two deductive systems for the modal mucalculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a second infinitary calculus which is based on nonwellfounded trees. In this system proofs are finitely branching but may contain infinite branches as long as some greatest fixed point is unfolded infinitely often along every branch. The main contribution of our paper is a translation from proofs in the first system to proofs in the second system. Completeness of the second system then follows from completeness of the first, and a new proof of the finite model property also follows as corollary. 1
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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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
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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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
Fibrations and Calculi of Fractions
 Journal of pure and applied algebra
, 1994
"... Given a fibration E ! B and a class \Sigma of arrows of B, one can construct the free fibration (on E over B such that all reindexing functors over elements of \Sigma are equivalences. ..."
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Given a fibration E ! B and a class \Sigma of arrows of B, one can construct the free fibration (on E over B such that all reindexing functors over elements of \Sigma are equivalences.
µCalculus Model Checking in Maude
, 2004
"... In this paper, a rewrite theory for checking µcalculus properties is developed. We use the same framework proposed in [EMS02] and demonstrate how rewriting logic can be used as a unified formalism from model specification to verification algorithm implementation. Furthermore, since µcalculus is mo ..."
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Cited by 3 (2 self)
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In this paper, a rewrite theory for checking µcalculus properties is developed. We use the same framework proposed in [EMS02] and demonstrate how rewriting logic can be used as a unified formalism from model specification to verification algorithm implementation. Furthermore, since µcalculus is more expressive than LTL, this work can be seen as an extension to [EMS02] in theory. We also develop a CTL to µcalculus translator to help users write CTL specifications more easily. However, the corresponding LTL to µcalculus translator is missing. The LTL model checker in [EMS02] is still preferred in practice.