Results 1  10
of
57
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
Abstract

Cited by 481 (20 self)
 Add to MetaCart
Least fixpoints as meanings of recursive definitions.
Automata with group actions
 In LICS
, 2011
"... Abstract—Our motivating question is a MyhillNerode theorem for infinite alphabets. We consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order. We develop a framework for studying such alp ..."
Abstract

Cited by 18 (6 self)
 Add to MetaCart
(Show Context)
Abstract—Our motivating question is a MyhillNerode theorem for infinite alphabets. We consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order. We develop a framework for studying such alphabets, where the key role is played by the automorphism group of the alphabet. This framework builds on the idea of nominal sets of Gabbay and Pitts; nominal sets are the special case of our framework where letters can be only compared for equality. We use the framework to uniformly generalize to infinite alphabets parts of automata theory, including decidability results. In the case of letters compared for equality, we obtain automata equivalent in expressive power to finite memory automata, as defined by Francez and Kaminski. I.
Automata and fixed point logics: a coalgebraic perspective
 Electronic Notes in Theoretical Computer Science
, 2004
"... This paper generalizes existing connections between automata and logic to a coalgebraic level. Let F: Set → Set be a standard functor that preserves weak pullbacks. We introduce various notions of Fautomata, devices that operate on pointed Fcoalgebras. The criterion under which such an automaton a ..."
Abstract

Cited by 16 (8 self)
 Add to MetaCart
(Show Context)
This paper generalizes existing connections between automata and logic to a coalgebraic level. Let F: Set → Set be a standard functor that preserves weak pullbacks. We introduce various notions of Fautomata, devices that operate on pointed Fcoalgebras. The criterion under which such an automaton accepts or rejects a pointed coalgebra is formulated in terms of an infinite twoplayer graph game. We also introduce a language of coalgebraic fixed point logic for Fcoalgebras, and we provide a game semantics for this language. Finally we show that any formula p of the language can be transformed into an Fautomaton Ap which is equivalent to p in the sense that Ap accepts precisely those pointed Fcoalgebras in which p holds.
Coalgebraic automata theory: Basic results
 Logical Methods in Computer Science
"... Vol. 4 (4:10) 2008, pp. 1–43 www.lmcsonline.org ..."
(Show Context)
Closure properties of coalgebra automata
 in: LICS 2005 [1
"... We generalize some of the central results in automata theory to the abstraction level of coalgebras. In particular, we show that for any standard, weak pullback preserving functor F, the class of recognizable languages of Fcoalgebras is closed under taking unions, intersections and projections. ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
(Show Context)
We generalize some of the central results in automata theory to the abstraction level of coalgebras. In particular, we show that for any standard, weak pullback preserving functor F, the class of recognizable languages of Fcoalgebras is closed under taking unions, intersections and projections. Our main technical result concerns a construction which transforms a given alternating Fautomaton into an equivalent nondeterministic one. 1.
The category theoretic solution of recursive program schemes
 Proc. First Internat. Conf. on Algebra and Coalgebra in Computer Science (CALCO 2005), Lecture Notes in Computer Science
, 2006
"... Abstract. This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the categorytheoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: worki ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
Abstract. This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the categorytheoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: working only in categories with “enough final coalgebras ” we show how to formulate, solve, and study recursive program schemes. Our general theory is algebraic and so avoids using ordered, or metric structures. Our work generalizes the previous approaches which do use this extra structure by isolating the key concepts needed to study substitution in infinite trees, including secondorder substitution. As special cases of our interpreted solutions we obtain the usual denotational semantics using complete partial orders, and the one using complete metric spaces. Our theory also encompasses implicitly defined objects which are not usually taken to be related to recursive program schemes. For example, the classical Cantor twothirds set falls out as an interpreted
Strongly complete logics for coalgebras
, 2006
"... Coalgebras for a functor T on a category X model many different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary strongly complete specification languages for Setbased coalgebras. We show how to associate a finitary logic to any finitesets preservin ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
Coalgebras for a functor T on a category X model many different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary strongly complete specification languages for Setbased coalgebras. We show how to associate a finitary logic to any finitesets preserving functor T and prove the logic to be strongly complete under a mild condition on T. The proof is based on the following result. An endofunctor on a variety has a presentation by operations and equations iff it preserves sifted colimits. 1
Free modal algebras: a coalgebraic perspective
"... Abstract. In this paper we discuss a uniform method for constructing free modal and distributive modal algebras. This method draws on works by (Abramsky 2005) and (Ghilardi 1995). We revisit the theory of normal forms for modal logic and derive a normal form representation for positive modal logic. ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we discuss a uniform method for constructing free modal and distributive modal algebras. This method draws on works by (Abramsky 2005) and (Ghilardi 1995). We revisit the theory of normal forms for modal logic and derive a normal form representation for positive modal logic. We also show that every finitely generated free modal and distributive modal algebra axiomatised by equations of rank 1 is a reduct of a temporal algebra. 1
Modal Predicates and Coequations
, 2002
"... We show how coalgebras can be presented by operations and equations. We discuss the basic properties of this presentation and compare it with the usual approach. ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We show how coalgebras can be presented by operations and equations. We discuss the basic properties of this presentation and compare it with the usual approach.