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Enhanced Coalgebraic Bisimulation
, 2013
"... We present a systematic study of bisimulation-up-to 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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We present a systematic study of bisimulation-up-to 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 context-free languages
- Logical Methods in Computer Science
"... Abstract. In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final coalgebra semantics then gives an interpretation fu ..."
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Abstract. In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative 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 term-algebra; 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 so-called syntactic solution method and abstract GSOS.
On language equations and grammar coalgebras for context-free languages?
"... Introduction. In [3], a coalgebraic presentation of context-free grammars and languages was given based on behavioural differential equation, yielding final coalgebra semantics via the functor 2 × (−)A of deterministic automata. There, the correspondence was given via the well-known notion of deriva ..."
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Introduction. In [3], a coalgebraic presentation of context-free grammars and languages was given based on behavioural differential equation, yielding final coalgebra semantics via the functor 2 × (−)A of deterministic automata. There, the correspondence was given via the well-known notion of derivations in a grammar. Another classical approach to the semantics of context-free gram-
A completeness result for finite λ-bisimulations
"... Abstract. We show that finite λ-bisimulations (closely related to bisim-ulations up to context) are sound and complete for finitely generated λ-bialgebras for distributive laws λ of a monad T on Set over an end-ofunctor F on Set, such that F preserves weak pullbacks and finitely generated T-algebras ..."
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Abstract. We show that finite λ-bisimulations (closely related to bisim-ulations up to context) are sound and complete for finitely generated λ-bialgebras for distributive laws λ of a monad T on Set over an end-ofunctor F on Set, such that F preserves weak pullbacks and finitely generated T-algebras are closed under taking kernel pairs. This result is used to infer the decidability of weighted language equivalence when the underlying semiring is a subsemiring of an effectively presentable Noetherian semiring. These results are closely connected to [ÉM10] and [BMS13], concerned with respectively the decidability and axiomatiza-tion of weighted language equivalence w.r.t. Noetherian semirings. 1
1 Errata 1. p. 4, fourth line above Section 1.2: ‘abstract GSOS format, based on the SOS format
"... from [TP97] ’ should be ‘abstract GSOS format introduced in [TP97], generalizing the (concrete) GSOS format from [BIM95]’. 2. p. 5, point 3 of the enumeration in Subsection 1.2.2: ‘Kleene-Schützenberger-Eilenberg theorem ’ should be ‘Kleene-Schützenberger theorem’. 3. p. 7, second paragraph of Sec ..."
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from [TP97] ’ should be ‘abstract GSOS format introduced in [TP97], generalizing the (concrete) GSOS format from [BIM95]’. 2. p. 5, point 3 of the enumeration in Subsection 1.2.2: ‘Kleene-Schützenberger-Eilenberg theorem ’ should be ‘Kleene-Schützenberger theorem’. 3. p. 7, second paragraph of Section 1.3: ‘due to Kleene, Schützenberger, and Eilenberg’ should be ‘due to Kleene and Schützenberger’. 4. p. 7, l.-5: ‘bisimulations up to linear combinations ’ should be ‘bisimulations up to linearity ’. 5. p. 7, l.-3: ‘linear weighted simulations ’ should be ‘linear weighted bisimulations’. 6. p. 11, l. 5: ‘and have been used’, should be ‘which have been used’. 7. p. 11, last paragraph: ‘Kleene-Schützenberger-Eilenberg theorem ’ should be ‘Kleene-
COALGEBRAIC CHARACTERIZATIONS OF CONTEXT-FREE LANGUAGES
, 2012
"... Vol. 9(3:14)2013, pp. 1–39 www.lmcs-online.org ..."
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