Displaying similar documents to “On shuffle ideals”

Minimal NFA and biRFSA languages

Michel Latteux, Yves Roos, Alain Terlutte (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In this paper, we define the notion of biRFSA which is a residual finate state automaton (RFSA) whose the reverse is also an RFSA. The languages recognized by such automata are called biRFSA languages. We prove that the canonical RFSA of a biRFSA language is a minimal NFA for this language and that each minimal NFA for this language is a sub-automaton of the canonical RFSA. This leads to a characterization of the family of biRFSA languages. In the second part of this paper, we define...

How expressions can code for automata

Sylvain Lombardy, Jacques Sakarovitch (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. We show here that if an automaton is then sufficiently “decorated”, the combination of these...

Corrigendum to our paper: How Expressions Can Code for Automata

Sylvain Lombardy, Jacques Sakarovitch (2010)

RAIRO - Theoretical Informatics and Applications

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In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms...

Series which are both max-plus and min-plus rational are unambiguous

Sylvain Lombardy, Jean Mairesse (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Consider partial maps Σ * → ℝ with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure to build an unambiguous automaton from a max-plus automaton and a min-plus one...

Returning and non-returning parallel communicating finite automata are equivalent

Ashish Choudhary, Kamala Krithivasan, Victor Mitrana (2007)

RAIRO - Theoretical Informatics and Applications

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A parallel communicating automata system consists of several automata working independently in parallel and communicating with each other by request with the aim of recognizing a word. Rather surprisingly, returning parallel communicating finite automata systems are equivalent to the non-returning variants. We show this result by proving the equivalence of both with multihead finite automata. Some open problems are finally formulated.