Separating words with machines and groups
Sequential mappings of -languages
Sequential monotonicity for restarting automata
As already 2-monotone R-automata accept NP-complete languages, we introduce a restricted variant of j-monotonicity for restarting automata, called sequential j-monotonicity. For restarting automata without auxiliary symbols, this restricted variant still yields infinite hierarchies. However, for restarting automata with auxiliary symbols, all degrees of sequential monotonicity collapse to the first level, implying that RLWW-automata that are sequentially monotone of degree j for any j ≥ 1 only...
Séries algébriques solutions d'équations linéaires avec opérateurs
Séries formelles
La classification chomskienne des langages formels conduit à l'étude d'objets mathématiques nouveaux: les séries rationnelles et algébriques en variables non commutatives.
Séries formelles rationnelles et reconnaissables
Séries rationnelles
Séries rationnelles à plusieurs variables non commutatives, Hadamard-inversibles
Series which are both max-plus and min-plus rational are unambiguous
Consider partial maps 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...
Series which are both max-plus and min-plus rational are unambiguous
Consider partial maps ∑* → 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 that recognize the same series.
Set-theoretical operations on -multiple languages
Similarity relations and cover automata
Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...
Similarity relations and cover automata
Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...
Simple automata
Simulation of dynamic systems with a transfer function of the type m=n excited by the Dirac function
Single-tape reset machines
Solid codes and disjunctive domains.
Some Algebraic Properties of Machine Poset of Infinite Words
The complexity of infinite words is considered from the point of view of a transformation with a Mealy machine that is the simplest model of a finite automaton transducer. We are mostly interested in algebraic properties of the underlying partially ordered set. Results considered with the existence of supremum, infimum, antichains, chains and density aspects are investigated.
Some algorithms on the star operation applied to finite languages.
Some arithmetical theorems on base conversions