Context-Free Languages, Coalgebraically

Winter, Joost de; Bonsangue, Marcello M.; Rütten, Jan

doi:10.1007/978-3-642-22944-2_25

Cited by 16 publications

(24 citation statements)

References 14 publications

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“…This gives the expected correspondence between two of the three different coalgebraic approaches to context-free languages introduced in [38] (the third approach is about fixed-point expressions and as such is outside the scope of this paper). ⊳ Similarly, the algebraic structure induced by λ on the final F -coalgebra factors uniquely through the algebraic structure induced by κ.…”

Section: Morphisms and Solutionsmentioning

confidence: 91%

Presenting Distributive Laws

Bonsangue

Hansen

Kurz

et al. 2013

Algebra and Coalgebra in Computer Science

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Abstract. Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved 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 context-free languages.

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Section: Morphisms and Solutionsmentioning

confidence: 91%

Presenting Distributive Laws

Bonsangue

Hansen

Kurz

et al. 2013

Algebra and Coalgebra in Computer Science

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“…The associated coalgebra o, t : 1 → F T 1 is given by The above characterization of context free languages over an alphabet A is different and complementary to the coalgebraic account of context-free languages presented in [44]. The latter, in fact, uses the functor D(X) = 2 × X A for deterministic automata (instead of the Moore automata with output in 2 B * above, for B a set of variables), and the idempotent semiring monad T (X) = P ω ((X + A) * ) (instead of our side effect monad) to study different but equivalent ways to present context-free languages: using grammars, behavioural differential equations and generalized regular expressions in which the Kleene star is replaced by a unique fixed point operator.…”

Section: T T T T T T T T T T T T T T T T T Tmentioning

confidence: 99%

Generalizing determinization from automata to coalgebras

Silva¹,

Bonchi²,

Bonsangue³

et al. 2013

Logical Methods in Computer Science

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Abstract. The powerset construction is a standard method for converting a nondeterministic automaton into a deterministic one recognizing the same language. In this paper, we lift the powerset construction from automata to the more general framework of coalgebras with structured state spaces. Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (F -coalgebras) and a notion of behavioural equivalence (∼F ) amongst them. Many types of transition systems and their equivalences can be captured by a functor F . For example, for deterministic automata the derived equivalence is language equivalence, while for non-deterministic automata it is ordinary bisimilarity.We give several examples of applications of our generalized determinization construction, including partial Mealy machines, (structured) Moore automata, Rabin probabilistic automata, and, somewhat surprisingly, even pushdown automata. To further witness the generality of the approach we show how to characterize coalgebraically several equivalences which have been object of interest in the concurrency community, such as failure or ready semantics. ACM CCS

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“…This format is an adaptation and extension of the formats presented in [WBR11] and [BRW12]. As we will show later in this article, the formal power series characterizable in this way correspond exactly to various notions of algebraic power series.…”

Section: Context-free Systemsmentioning

confidence: 99%

“…In [WBR11], we extended this coalgebraic picture further, giving a characterization of the context-free languages as solutions to systems of behavioural differential equations, in which all Brzozowski derivatives are presented as polynomials over the set of variables, and in [BRW12], we have generalized the theory to formal power series in noncommuting variables, providing a new characterization of so-called algebraic or context-free power series, coinciding with the familiar generalization from context-free languages to algebraic power series.…”

Section: Introductionmentioning

confidence: 99%

Context-free coalgebras

Winter¹,

Bonsangue²,

Rütten³

2015

Journal of Computer and System Sciences

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In this article, we provide a coalgebraic account of parts of the mathematical theory underlying context-free languages. We characterize context-free languages, and power series and streams generalizing or corresponding to the context-free languages, by means of systems of behavioural differential equations; and prove a number of results, some of which are new, and some of which are new proofs of existing theorems, using the techniques of bisimulation and bisimulation up to linear combinations. Furthermore, we establish a link between automatic sequences and these systems of equations, allowing us to, given an automaton generating an automatic sequence, easily construct a system of behavioural differential equations yielding this sequence as a context-free stream.

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Context-Free Languages, Coalgebraically

Cited by 16 publications

References 14 publications

Presenting Distributive Laws

Presenting Distributive Laws

Generalizing determinization from automata to coalgebras

Context-free coalgebras

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