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224
A Coinduction Principle for Recursive Data Types Based on Bisimulation
, 1996
"... This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programmin ..."
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Cited by 37 (3 self)
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This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programming languages [SS71], but also arise explicitly as recursive data types in functional programming languages like Standard ML [MTH90] or Haskell [HPJW92]. In the latter context, the coinduction principle provides a powerful technique for establishing the equality of programs with values in recursive data types (see examples herein and in [Pit94]).
DYNAMIC CONGRUENCE vs. PROGRESSING BISIMULATION for CCS
 Fundamenta Informaticae
, 1992
"... 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. ff:ø:fi:nil and ff:fi:nil are woc but ø:fi:nil and fi:nil are not. This fact prevent us from characterizing CCS s ..."
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Cited by 36 (12 self)
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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. ff:ø:fi:nil and ff:fi:nil are woc but ø:fi:nil and fi:nil are not. This fact prevent us from characterizing CCS semantics (when ø 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 Bisimulatio...
Features and Formulae
, 1991
"... This paper shows how these structures can be axiomatized in a decidable class of firstorder logic, which can also be used to express constraints on these structures. Desirable properties, such as compactness and decidability, follow directly. Moreover, additional types of feature values, such as &q ..."
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Cited by 27 (1 self)
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This paper shows how these structures can be axiomatized in a decidable class of firstorder logic, which can also be used to express constraints on these structures. Desirable properties, such as compactness and decidability, follow directly. Moreover, additional types of feature values, such as "setvalued" features, can be incorporated into the system simply by axiomatizing their properties
Distributivity for Endofunctors, Pointed and CoPointed Endofunctors, Monads and Comonads
, 2000
"... We generalise the notion of a distributive law between a monad and a comonad to consider weakened structures such as pointed or copointed endofunctors, or endofunctors. We investigate EilenbergMoore and Kleisli constructions for each of these possibilities. Then we consider two applications of the ..."
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Cited by 26 (1 self)
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We generalise the notion of a distributive law between a monad and a comonad to consider weakened structures such as pointed or copointed endofunctors, or endofunctors. We investigate EilenbergMoore and Kleisli constructions for each of these possibilities. Then we consider two applications of these weakened notions of distributivity in detail. We characterise Turi and Plotkin's model of GSOS as a distributive law of a monad over a copointed endofunctor, and we analyse generalised coiteration and coalgebraic coinduction \upto" in terms of a distributive law of the underlying pointed endofunctor of a monad over an endofunctor. 1 Work supported by Esprit Working Group \Types", MURST'99 Con. \Sistemi Formali. .." grant. 2 This work is supported by EPSRC grants GR/J84205: Frameworks for programming language semantics and logic and GR/M56333: The structure of programming languages : syntax and semantics, and British Council grant 747 FCS R34807: Data and program renement using alg...
On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers
 In Proceedings of the First International Conference on Principles and Practice of Constraint Programming
"... When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint sol ..."
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Cited by 26 (3 self)
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When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a "free amalgamated product" as a possible solution to the first problem. Subsequently, we define socalled simplycombinable structures (SCstructures). For SCstructures over disjoint signatures, a canonical amalgamation construction exists, which for the subclass of strong SCstructures yields the free amalgamated product. The combination technique of [BS92, BaS94a] can be used to combine constraint solvers for (strong) SCstructures over disjoint signatures into a solver for their (free) amalgamated product. In addition to term algebras modulo equational theories, the class of SCstru...
Hypercomputation and the Physical ChurchTuring Thesis
, 2003
"... A version of the ChurchTuring Thesis states that every e#ectively realizable physical system can be defined by Turing Machines (`Thesis P'); in this formulation the Thesis appears an empirical, more than a logicomathematical, proposition. We review the main approaches to computation beyond Tu ..."
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Cited by 21 (0 self)
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A version of the ChurchTuring Thesis states that every e#ectively realizable physical system can be defined by Turing Machines (`Thesis P'); in this formulation the Thesis appears an empirical, more than a logicomathematical, proposition. We review the main approaches to computation beyond Turing definability (`hypercomputation'): supertask, nonwellfounded, analog, quantum, and retrocausal computation. These models depend on infinite computation, explicitly or implicitly, and appear physically implausible; moreover, even if infinite computation were realizable, the Halting Problem would not be a#ected. Therefore, Thesis P is not essentially di#erent from the standard ChurchTuring Thesis.
Back and forth bisimulations
 Computer Science Report CS R9021, Centrum voor Wiskunde en Informatica
, 1990
"... This paper is concerned with bisimulation relations which do not only require related agents to simulate each others behavior in the direction of the arrows, but also to simulate each other when going back in history. First it is demonstrated that the back and forth variant of strong bisimulation le ..."
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Cited by 21 (2 self)
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This paper is concerned with bisimulation relations which do not only require related agents to simulate each others behavior in the direction of the arrows, but also to simulate each other when going back in history. First it is demonstrated that the back and forth variant of strong bisimulation leads to the same equivalence as the ordinary notion of strong bisimulation. Then it is shown that the back and forth variant of Milner's observation equivalence is different from (and finer than) observation equivalence. In fact we prove that it coincides with the branching bisimulation equivalence of Van Glabbeek & Weijland. Also the back and forth variants of branching, ~ and delay bisimulation lead to branching bisimulation equivalence. The notion of back and forth bisimulation moreover leads to characterizations of branching bisimulation in terms of abstraction homomorphisms and in terms of HencessyMilner logic with backward modalities. In our view these results support the claim that branching bisimulation is a natural and important notion. The notion of bisimulation relation has been introduced by PARK [18]. It leads to an equivalence on labelled transition systems which, in case image finiteness is assumed, coincides with the strong equivalence of ~IILNER [12]. The great importance and usefulness of bisimulalions
A Logical Treatment of SemiFree Word Order and Bounded Discontinuous Constituency
, 1989
"... free word order and bounded discontinuous constituency. We extend standard feature value logics to treat word order in a single formalism with a rigorous semantics without phrase structure rules. The elimination of phrase structure rules allows a natural generalisation of the approach to nonconfigur ..."
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Cited by 20 (0 self)
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free word order and bounded discontinuous constituency. We extend standard feature value logics to treat word order in a single formalism with a rigorous semantics without phrase structure rules. The elimination of phrase structure rules allows a natural generalisation of the approach to nonconfigurational word order and bounded discontinuous continuency via sequence union. Sequence union formalises the notions of clause union and scrambling by providing a mechanism for describing word order domains larger than the local tree. The formalism incorporates the distinction between bounded and unbounded forms of discontinuous constituency. Grammars are organised as algebraic theories. This means that linguistic generalisations are stated as axioms about the structure of signs. This permits a natural interpretation of implicational universals in terms of theories, subtheories and implicational axioms. The accompanying linguistic analysis is eclectic, borrowing insights from many current linguistic theories.
From bisimulation to simulation: coarsest partition problems
 J. Automated Reasoning
, 2003
"... Abstract. The notions of bisimulation and simulation are used for graph reduction and are widely employed in many areas: modal logic, concurrency theory, set theory, formal verification, and so forth. In particular, in the context of formal verification they are used to tackle the socalled stateex ..."
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Cited by 19 (1 self)
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Abstract. The notions of bisimulation and simulation are used for graph reduction and are widely employed in many areas: modal logic, concurrency theory, set theory, formal verification, and so forth. In particular, in the context of formal verification they are used to tackle the socalled stateexplosion problem. The faster algorithms to compute the maximum bisimulation on a given labeled graph are based on the crucial equivalence between maximum bisimulation and relational coarsest partition problem. As far as simulation is concerned, many algorithms have been proposed that turn out to be relatively inexpensive in terms of either time or space. In this paper we first revisit the state of the art about bisimulation and simulation, pointing out the analogies and differences between the two problems. Then, we propose a generalization of the relational coarsest partition problem, which is equivalent to the simulation problem. Finally, we present an algorithm that exploits such a characterization and improves on previously proposed algorithms for simulation. Key words: bisimulation, simulation, partition refinement problems. 1.