Results 1  10
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21
Coalgebraic BisimulationUpTo
, 2013
"... Bisimulationupto enhances the bisimulation proof method for process equivalence. We present its generalization from labelled transition systems to arbitrary coalgebras, and show that for a large class of systems, enhancements such as bisimulation up to bisimilarity, up to equivalence and up to con ..."
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Cited by 17 (7 self)
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Bisimulationupto enhances the bisimulation proof method for process equivalence. We present its generalization from labelled transition systems to arbitrary coalgebras, and show that for a large class of systems, enhancements such as bisimulation up to bisimilarity, up to equivalence and up to context are sound proof techniques. This allows for simplified bisimulation proofs for many different types of statebased systems.
Presenting distributive laws
 In CALCO
, 2013
"... Abstract. Distributive laws of a monad T over a functor F are categorical tools for specifying algebracoalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of wellbehaved structural operational semantics and, more recently, also fo ..."
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Cited by 8 (4 self)
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Abstract. Distributive laws of a monad T over a functor F are categorical tools for specifying algebracoalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of wellbehaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of contextfree languages. 1
Nature
, 1993
"... We present a format for the specification of probabilistic transition systems that guarantees that bisimulation equivalence is a congruence for any operator defined in this format. In this sense, the format is somehow comparable to the ntyft/ntyxt format in a nonprobabilistic setting. We also study ..."
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Cited by 4 (0 self)
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We present a format for the specification of probabilistic transition systems that guarantees that bisimulation equivalence is a congruence for any operator defined in this format. In this sense, the format is somehow comparable to the ntyft/ntyxt format in a nonprobabilistic setting. We also study the modular construction of probabilistic transition systems specifications and prove that some standard conservative extension theorems also hold in our setting. Finally, we show that the trace congruence for imagefinite processes induced by our format is precisely bisimulation on probabilistic systems. Note:
Enhanced Coalgebraic Bisimulation
, 2013
"... We present a systematic study of bisimulationupto techniques for coalgebras. This enhances the bisimulation proof method for a large class of state based systems, including labelled transition systems but also stream systems and weighted automata. Our approach allows for compositional reasoning ab ..."
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Cited by 4 (3 self)
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We present a systematic study of bisimulationupto techniques for coalgebras. This enhances the bisimulation proof method for a large class of state based systems, including labelled transition systems but also stream systems and weighted automata. Our approach allows for compositional reasoning about the soundness of enhancements. Applications include the soundness of bisimulation up to bisimilarity, up to equivalence and up to congruence. All in all, this gives a powerful and modular framework for simplified coinductive proofs of equivalence. 1.
Coalgebraic characterizations of contextfree languages
 Logical Methods in Computer Science
"... Abstract. In this article, we provide three coalgebraic characterizations of the class of contextfree languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying outputderivative pairs. Final coalgebra semantics then gives an interpretation fu ..."
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Cited by 3 (3 self)
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Abstract. In this article, we provide three coalgebraic characterizations of the class of contextfree languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying outputderivative pairs. Final coalgebra semantics then gives an interpretation function into the final coalgebra of all languages with the usual output and derivative operations. The first characterization is based on systems, where each derivative is given as a finite language over the set of nonterminals; the second characterization on systems where derivatives are given as elements of a termalgebra; and the third characterization is based on adding coalgebraic structure to a class of closed (unique) fixed point expressions. We prove equivalences between these characterizations, discuss the generalization from languages to formal power series, as well as the relationship to the generalized powerset construction. 1.
Stream Differential Equations: Specification Formats and Solution Methods
, 2014
"... Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been dev ..."
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Cited by 2 (2 self)
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Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been developed in many papers over the past two decades. In this paper we present a survey of the many results in this area. Our focus is on the classification of different formats of stream differential equations, their solution methods, and the classes of streams they can define. Moreover, we describe in detail the connection between the socalled syntactic solution method and abstract GSOS.
Coalgebraic upto techniques
"... A simple algorithm for checking language equivalence of finite automata consists in trying to compute a bisimulation that relates them. This is possible because language equivalence can be characterised coinductively, as the largest bisimulation. More precisely, consider an automaton 〈S, t, o〉, whe ..."
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A simple algorithm for checking language equivalence of finite automata consists in trying to compute a bisimulation that relates them. This is possible because language equivalence can be characterised coinductively, as the largest bisimulation. More precisely, consider an automaton 〈S, t, o〉, where S is a (finite) set of states, t: S → P(S)A is a nondeterministic transition function, and o: S → 2 is the characteristic function of the set of accepting states. Such an automation gives rise to a determinised automaton 〈P(S), t], o]〉, where t] : P(S) → P(S)A and o] : P(S) → 2 are the natural extensions of t and o to sets. A bisimulation is a relation R between sets of states such that for all sets of states X,Y, X R Y entails: 1. o](X) = o](Y), and 2. for all letter a, t]a(X) R t a(Y). The coinductive characterisation is the following one: two sets of states recognise the same language if and only if they are related by some bisimulation. Taking inspiration from concurrency theory [4,5], one can improve this proof technique by weakening the second item in the definition of bisimulation: given a function f on binary relations, a bisimulation up to f is a relation R between states such that for all sets X,Y, X R Y entails: 1. o](X) = o](Y), and 2. for all letter a, t]a(X) f(R) t a(Y). For wellchosen functions f, bisimulations up to f are contained in a bisimulation, so that the improvement is sound. So is the function mapping each relation to its equivalence closure. In this particular case, one recover the standard algorithm by Hopcroft and Karp [2]: two sets can be skipped whenever they can already be related by a sequence of pairwise related states. One can actually do more, by considering the function c mapping each relation to its congruence closure: the smallest equivalence relation which contains
Foundational Extensible Corecursion
, 2014
"... This paper presents a theoretical framework for defining corecursive functions safely in a total setting, based on corecursion upto and relational parametricity. The end product is a general corecursor that allows corecursive (and even recursive) calls under wellbehaved operations, including con ..."
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Cited by 1 (1 self)
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This paper presents a theoretical framework for defining corecursive functions safely in a total setting, based on corecursion upto and relational parametricity. The end product is a general corecursor that allows corecursive (and even recursive) calls under wellbehaved operations, including constructors. Corecursive functions that are well behaved can be registered as such, thereby increasing the corecursor’s expressiveness. To the extensible corecursor corresponds an equally flexible coinduction principle. The metatheory is formalized in the Isabelle proof assistant and forms the core of a prototype tool. The approach is foundational: The corecursor is derived from first principles, without requiring new axioms or extensions of the logic. This ensures that no inconsistencies can be introduced by omissions in a termination or productivity check.
Structural Operational Semantics for Stochastic and Weighted Transition Systems
, 2013
"... We introduce weighted GSOS, a general syntactic framework to specify wellbehaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the ..."
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We introduce weighted GSOS, a general syntactic framework to specify wellbehaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the flexibility of the framework by instantiating it to handle some special cases, most notably that of stochastic transition systems. Through examples we provide weightedGSOS definitions for common stochastic operators in the literature.
Initial Algebras of Terms, with binding and algebraic structure
, 2013
"... Abstract. One of the many results which makes Joachim Lambek famous is: an initial algebra of an endofunctor is an isomorphism. This fixed point result is often referred to as “Lambek’s Lemma”. In this paper, we illustrate the power of initiality by exploiting it in categories of algebravalued pres ..."
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Abstract. One of the many results which makes Joachim Lambek famous is: an initial algebra of an endofunctor is an isomorphism. This fixed point result is often referred to as “Lambek’s Lemma”. In this paper, we illustrate the power of initiality by exploiting it in categories of algebravalued presheaves EM(T)N, for a monad T on Sets. The use of presheaves to obtain certain calculi of expressions (with variable binding) was introduced by Fiore, Plotkin, and Turi. They used setvalued presheaves, whereas here the presheaves take values in a category EM(T) of EilenbergMoore algebras. This generalisation allows us to develop a theory where more structured calculi can be obtained. The use of algebras means also that we work in a linear context and need a separate operation! for replication, for instance to describe strength for an endofunctor on EM(T). We apply the resulting theory to give systematic descriptions of nontrivial calculi: we introduce nondeterministic and weighted lambda terms and expressions for automata as initial algebras, and we formalise relevant equations diagrammatically. 1