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Algebraic specification and coalgebraic synthesis of Mealy machines
 In: Proceedings of FACS 2005. ENTCS
, 2006
"... We introduce the notion of functional stream derivative, generalising the notion of input derivative of rational expressions (Brzozowski 1964) to the case of stream functions over arbitrary input and output alphabets. We show how to construct Mealy automata from algebraically specified stream functi ..."
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Cited by 19 (7 self)
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We introduce the notion of functional stream derivative, generalising the notion of input derivative of rational expressions (Brzozowski 1964) to the case of stream functions over arbitrary input and output alphabets. We show how to construct Mealy automata from algebraically specified stream functions by the symbolic computation of functional stream derivatives. We illustrate this construction in full detail for various bitstream functions specified in the algebraic calculus of the 2adic numbers. This work is part of a larger ongoing effort to specify and model component connector circuits in terms of (functions and relations on) streams.
Rational and recognisable power series
 DRAFT OF A CHAPTER FOR THE HANDBOOK OF WEIGHTED AUTOMATA
"... ..."
A Unified Construction of the Glushkov, Follow, and Antimirov Automata
 Proc. of MFCS’06, LNCS 4162
, 2006
"... Abstract. A number of different techniques have been introduced in the last few decades to create ɛfree automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods bo ..."
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Cited by 6 (0 self)
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Abstract. A number of different techniques have been introduced in the last few decades to create ɛfree automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods both for unweighted and weighted regular expressions. It describes simpler algorithms with time complexities at least as favorable as that of the best previously known techniques, and provides a concise proof of their correctness. Our algorithms are all based on two standard automata operations: epsilonremoval and minimization. This contrasts with the multitude of complicated and specialpurpose techniques previously described in the literature, and makes it straightforward to generalize these algorithms to the weighted case. In particular, we extend the definition and construction of follow automata to the case of weighted regular expressions over a closed semiring and present the first algorithm to compute weighted Antimirov automata. 1
On the equivalence of Zautomata
 In ICALP 2005 (2005
"... Abstract. We prove that two automata with multiplicity in Z are equivalent, i.e. define the same rational series, if and only if there is a sequence of Zcoverings, coZcoverings, and circulations of −1, which transforms one automaton into the other. Moreover, the construction of these transformati ..."
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Cited by 4 (2 self)
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Abstract. We prove that two automata with multiplicity in Z are equivalent, i.e. define the same rational series, if and only if there is a sequence of Zcoverings, coZcoverings, and circulations of −1, which transforms one automaton into the other. Moreover, the construction of these transformations is effective. This is obtained by combining two results: the first one relates coverings to conjugacy of automata, and is modeled after a theorem from symbolic dynamics; the second one is an adaptation of Schützenberger’s reduction algorithm of representations in a field to representations in an Euclidean domain (and thus in Z). 1
Inside Vaucanson
 In Proceedings of Implementation and Application of Automata, 10th International Conference (CIAA), Sophia Antipolis
, 2005
"... Abstract. This paper presents some features of the Vaucanson platform. We describe some original algorithms on weighted automata and transducers (computation of the quotient, conversion of a regular expression into a weighted automaton, and composition). We explain how complex declarations due to th ..."
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Cited by 2 (1 self)
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Abstract. This paper presents some features of the Vaucanson platform. We describe some original algorithms on weighted automata and transducers (computation of the quotient, conversion of a regular expression into a weighted automaton, and composition). We explain how complex declarations due to the generic programming are masked from the user and finally we present a proposal for an XML format that allows implicit descriptions for simple types of automata. 1
Symbolic Synthesis of Mealy Machines from Arithmetic Bitstream Functions
"... In this paper, we describe a symbolic synthesis method which given an algebraic expression that specifies a bitstream function f, constructs a (minimal) Mealy machine that realises f. The synthesis algorithm can be seen as an analogue of Brzozowski’s construction of a finite deterministic automaton ..."
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Cited by 1 (1 self)
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In this paper, we describe a symbolic synthesis method which given an algebraic expression that specifies a bitstream function f, constructs a (minimal) Mealy machine that realises f. The synthesis algorithm can be seen as an analogue of Brzozowski’s construction of a finite deterministic automaton from a regular expression. It is based on a coinductive characterisation of the operators of 2adic arithmetic in terms of stream differential equations. 1
The Differential Calculus of Bitstreams (Extended Abstract)
, 2004
"... Using (stream) differential equations for definitions and coinduction for proofs, we define, analyse, and relate in a uniform way four different algebraic structures on the set 2 of bitstreams, motivating each of them in terms of the digital circuits they can describe. ..."
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Using (stream) differential equations for definitions and coinduction for proofs, we define, analyse, and relate in a uniform way four different algebraic structures on the set 2 of bitstreams, motivating each of them in terms of the digital circuits they can describe.
Algorithms for Glushkov Kgraphs
, 2009
"... The automata arising from the well known conversion of regular expression to non deterministic automata have rather particular transition graphs. We refer to them as the Glushkov graphs, to honour his nice expressiontoautomaton algorithmic short cut [10]. The Glushkov graphs have been characterize ..."
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The automata arising from the well known conversion of regular expression to non deterministic automata have rather particular transition graphs. We refer to them as the Glushkov graphs, to honour his nice expressiontoautomaton algorithmic short cut [10]. The Glushkov graphs have been characterized [6] in terms of simple graph theoretical properties and certain reduction rules. We show how to carry, under certain restrictions, this characterization over to the weighted Glushkov graphs. With the weights in a semiring K, they are defined as the transition Glushkov Kgraphs of the Weighted Finite Automata (WFA) obtained by the generalized Glushkov construction [4] from the Kexpressions. It works provided that the semiring K is factorial and the Kexpressions are in the so called star normal form (SNF) of BrüggemanKlein [2]. The restriction to the factorial semiring ensures to obtain algorithms. The restriction to the SNF would not be necessary if every Kexpressions were equivalent to some with the same litteral length, as it is the case for the boolean semiring B but remains an open question for a general K.
MultiTildeBar Derivatives
"... Abstract. Multitildebar operators allow us to extend regular expressions. The associated extended expressions are compatible with the structure of Glushkov automata and they provide a more succinct representation than standard expressions. The aim of this paper is to examine the derivation of mult ..."
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Abstract. Multitildebar operators allow us to extend regular expressions. The associated extended expressions are compatible with the structure of Glushkov automata and they provide a more succinct representation than standard expressions. The aim of this paper is to examine the derivation of multitildebar expressions. Two types of computation are investigated: Brzozowski derivation and Antimirov derivation, as well as the construction of the associated automata. 1