Complexity in Prefix-Free Regular Languages

We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next provide the tight bounds on state complexity of symmetric difference, and deterministic and nondeterministic state complexity of difference and cyclic shift of prefix-free languages.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Brzozowski Algorithm Is Generically Super-Polynomial Deterministic Automata

International audienceWe study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. We prove that, for any d > 0, the probability that this number of states is greater than nd tends to 1 as n tends to infinity. As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for the uniform distribution on deterministic automata

Stability and Complexity of Minimising Probabilistic Automata

We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with floating-point arithmetic. Our algorithm can also be used for "lossy" minimisation with bounded error. We show an application in image compression. In the second part of the paper we study the complexity of the minimisation problem for probabilistic automata. We prove that the problem is NP-hard and in PSPACE, improving a recent EXPTIME-result.Comment: This is the full version of an ICALP'14 pape

A Kleene theorem for polynomial coalgebras

For polynomial functors G, we show how to generalize the classical notion of regular expression to G-coalgebras. We introduce a language of expressions for describing elements of the final G-coalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and finite G-coalgebras

Building the Minimal Automaton of A*X in Linear Time, When X Is of Bounded Cardinality

International audienceWe present an algorithm for constructing the minimal automaton recognizing A∗X, where the pattern X is a set of m (that is a fixed integer) non-empty words over a finite alphabet A whose sum of lengths is n. This algorithm, inspired by Brzozowski's minimization algorithm, uses sparse lists to achieve a linear time complexity with respect to n

HFST—Framework for Compiling and Applying Morphologies

HFST–Helsinki Finite-State Technology ( hfst.sf.net ) is a framework for compiling and applying linguistic descriptions with finite-state methods. HFST currently connects some of the most important finite-state tools for creating morphologies and spellers into one open-source platform and supports extending and improving the descriptions with weights to accommodate the modeling of statistical information. HFST offers a path from language descriptions to efficient language applications in key environments and operating systems. HFST also provides an opportunity to exchange transducers between different software providers in order to get the best out of each finite-state library.Peer reviewe

Partial derivative automata formalized in Coq

In this paper we present a computer assisted proof of the correctness of a partial derivative automata construction from a regular expression within the Coq proof assistant. This proof is part of a for- malization of Kleene algebra and regular languages in Coq towards their usage in program certification.Fundação para a Ciência e Tecnologia (FCT) Program POSI, RESCUE (PTDC/EIA/65862/2006), SFRH/BD/33233/2007

Probabilistic Reachability for Parametric Markov Models

Abstract. Given a parametric Markov model, we consider the problem of computing the formula expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is computed. Afterwards, this expression is evaluated to a closed form expression representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in an exponential growth of the regular expression relative to the number of states. We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids the exponential blow up in most practical cases. We give a detailed account of the approach, also extending to parametric models with rewards and with non-determinism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on non-trivial models.