Partial commutations and faithful rational transductions

Contextual partial commutations

We consider the monoid T with the presentation 〈a, b; aab = aba〉 which is “close” to trace monoids. We prove two different types of results. First, we give a combinatorial description of the lexicographically minimum and maximum representatives of their congruence classes in the free monoid {a, b}∗ and solve the classical equations, such as commutation and conjugacy in T. Then we study the clos...

Regular languages and partial commutations

The closure of a regular language under a [partial] commutation I has been extensively studied. We present new advances on two problems of this area: (1) When is the closure of a regular language under [partial] commutation still regular? (2) Are there any robust classes of languages closed under [partial] commutation? We show that the class Pol(G) of polynomials of group languages is closed un...

Iteration of rational transductions

The purpose of this paper is to show connections between iterated length preserving rational transductions and linear space computations Hence we study the smallest family of transductions containing length preserving rational transductions and closed under union composition and iteration We give several characterizations of this class using re stricted classes of length preserving rational tra...

Logical and Algebraic Characterizations of Rational Transductions

Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic con...

Solving Word Equations modulo Partial Commutations