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32
Weighted automata and weighted logics
 In Automata, Languages and Programming – 32nd International Colloquium, ICALP 2005
, 2005
"... Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speechtotext processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We g ..."
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Cited by 38 (7 self)
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Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speechtotext processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We generalize Büchi’s and Elgot’s fundamental theorems to this quantitative setting. We introduce a weighted version of MSO logic and prove that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with our weighted logic. We also consider weighted firstorder logic and show that aperiodic series coincide with the firstorder definable ones, if the semiring is locally finite, commutative and has some aperiodicity property. 1
Learning Functions Represented as Multiplicity Automata
, 2000
"... We study the learnability of multiplicity automata in Angluin’s exact learning model, and we investigate its applications. Our starting point is a known theorem from automata theory relating the ..."
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Cited by 26 (2 self)
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We study the learnability of multiplicity automata in Angluin’s exact learning model, and we investigate its applications. Our starting point is a known theorem from automata theory relating the
Compositional Analysis of Expected Delays in Networks of Probabilistic I/O Automata
, 1998
"... Probabilistic I/O automata (PIOA) constitute a model for distributed or concurrent systems that incorporates a notion of probabilistic choice. The PIOA model provides a notion of composition, for constructing a PIOA for a composite system from a collection of PIOAs representing the components. We pr ..."
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Cited by 17 (8 self)
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Probabilistic I/O automata (PIOA) constitute a model for distributed or concurrent systems that incorporates a notion of probabilistic choice. The PIOA model provides a notion of composition, for constructing a PIOA for a composite system from a collection of PIOAs representing the components. We present a method for computing completion probability and expected completion time for PIOAs. Our method is compositional, in the sense that it can be applied to a system of PIOAs, one component at a time, without ever calculating the global state space of the system (i.e. the composite PIOA). The method is based on symbolic calculations with vectors and matrices of rational functions, and it draws upon a theory of observables, which are mappings from delayed traces to real numbers that generalize the classical "formal power series " from algebra and combinatorics. Central to the theory is a notion of representation for an observable, which generalizes the clasical notion "linear representation " for formal power series. As in the classical case, the representable observables coincide with an abstractly defined class of "rational" observables; this fact forms the foundation of our method. 1
Implementation of a Compositional Performance Analysis Algorithm for Probabilistic I/O Automata
 IN PROCEEDINGS OF 1999 WORKSHOP ON PROCESS ALGEBRA AND PERFORMANCE MODELING (PAPM99). PRENSAS UNIVERSITARIAS DE
, 1999
"... In previous papers, we defined the probabilistic I/O automata model for specification and modeling of probabilistic concurrent systems, and we showed how certain performance measures for such systems could be computed compositionally, one component at a time, without the need for explicit constr ..."
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Cited by 11 (5 self)
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In previous papers, we defined the probabilistic I/O automata model for specification and modeling of probabilistic concurrent systems, and we showed how certain performance measures for such systems could be computed compositionally, one component at a time, without the need for explicit construction of the full global state space. In this paper, we report on our experiences in constructing and testing a computer implemention of these compositional analysis algorithms. Our implementation, which is coded in the functional programming language Standard ML, uses exact rational arithmetic to calculate performance measures, and it is also capable of producing symbolic rational function expressions that describe the dependence of performance measures on a system parameter.
Arithmetic Complexity, Kleene Closure, and Formal Power Series
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 8 (1999)
, 1999
"... The aim of this paper is to use formal power series techniques to study the structure of small arithmetic complexity classes such as GapNC 1 and GapL. More precisely, we apply the Kleene closure of languages and the formal power series operations of inversion and root extraction to these complexity ..."
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Cited by 7 (3 self)
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The aim of this paper is to use formal power series techniques to study the structure of small arithmetic complexity classes such as GapNC 1 and GapL. More precisely, we apply the Kleene closure of languages and the formal power series operations of inversion and root extraction to these complexity classes. We define a counting version of Kleene closure and show that it is intimately related to inversion and root extraction within GapNC 1 and GapL. We prove that Kleene closure, inversion, and root extraction are all hard operations in the following sense: There is a language in AC 0 for which inversion and root extraction are GapLcomplete, and there is a finite set for which inversion and root extraction are GapNC 1complete, with respect to appropriate reducibilities. The latter result raises the question of classifying finite languages so that their inverses fall within interesting subclasses of GapNC 1, such as GapAC 0. We initiate work in this direction by classifying the complexity of the Kleene closure of finite languages. We formulate the problem in terms of finite monoids and relate its complexity to the internal structure of the monoid.
Automata, Power Series, and Coinduction: taking input derivatives seriously (Extended Abstract)
, 1999
"... Formal power series, which are functions from the set of words over an alphabet A to a semiring k, are viewed coalgebraically. In summary, this amounts to supplying the set of all power series with a deterministic automaton structure, which has the universal property of being final. Finality then f ..."
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Cited by 6 (1 self)
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Formal power series, which are functions from the set of words over an alphabet A to a semiring k, are viewed coalgebraically. In summary, this amounts to supplying the set of all power series with a deterministic automaton structure, which has the universal property of being final. Finality then forms the basis for both definitions and proofs by coinduction, the coalgebraic counterpart of induction. Coinductive definitions of operators on power series take the shape of what we have called behavioural di#erential equations, after Brzozowski's notion of input derivative, and include many classical di#erential equations for analytic functions. The use of behavioural di#erential equations leads, amongst others, to easy definitions of and proofs about both existing and new operators on power series, as well as to the construction of finite (syntactic) nondeterministic automata, implementing them.
Čern´y’s conjecture and group representation theory
 J. Algebraic Combin
"... Abstract. Let us say that a Cayley graph Γ of a group G of order n is a Čern´y Cayley graph if every synchronizing automaton containing Γ as a subgraph with the same vertex set admits a synchronizing word of length at most (n − 1) 2. In this paper we use the representation theory of groups over the ..."
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Cited by 3 (1 self)
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Abstract. Let us say that a Cayley graph Γ of a group G of order n is a Čern´y Cayley graph if every synchronizing automaton containing Γ as a subgraph with the same vertex set admits a synchronizing word of length at most (n − 1) 2. In this paper we use the representation theory of groups over the rational numbers to obtain a number of new infinite families of Čern´y Cayley graphs. 1.
Mean asymptotic behaviour of radixrational sequences and dilation equations (Extended version
, 2008
"... Abstract. The generating series of a radixrational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radixrational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The ..."
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Cited by 2 (0 self)
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Abstract. The generating series of a radixrational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radixrational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic depends on the joint spectral radius of the linear representation of the sequence, and the coefficients are obtained through some dilation equations. The proofs are based on elementary linear algebra. Contents