scholarly journals Unambiguous Erasing Morphisms in Free Monoids

2009 ◽  
pp. 473-484 ◽  
Author(s):  
Johannes C. Schneider
Keyword(s):  
Free Monoids

A New Unavoidable Regularity in Free Monoids

Sequences II ◽  
1993 ◽  
pp. 447-456 ◽  
Author(s):  
Aldo de Luca ◽  
Stefano Varricchio
Keyword(s):  
Free Monoids

scholarly journals Solutions to twisted word equations and equations in virtually free groups

2020 ◽  
Vol 30 (04) ◽  
pp. 731-819
Author(s):  
Volker Diekert ◽  
Murray Elder
Keyword(s):  
Free Groups ◽  
Expressive Power ◽  
Solution Set ◽  
Complexity Bound ◽  
Free Monoids ◽  
Word Equation ◽  
All Solutions ◽  
Standard Normal ◽  
Word Equations ◽  
Solving Equations

It is well known that the problem solving equations in virtually free groups can be reduced to the problem of solving twisted word equations with regular constraints over free monoids with involution. In this paper, we prove that the set of all solutions of a twisted word equation is an EDT0L language whose specification can be computed in PSPACE . Within the same complexity bound we can decide whether the solution set is empty, finite, or infinite. In the second part of the paper we apply the results for twisted equations to obtain in PSPACE an EDT0L description of the solution set of equations with rational constraints for finitely generated virtually free groups in standard normal forms with respect to a natural set of generators. If the rational constraints are given by a homomorphism into a fixed (or “small enough”) finite monoid, then our algorithms can be implemented in [Formula: see text], that is, in quasi-quadratic nondeterministic space. Our results generalize the work by Lohrey and Sénizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to both complexity and expressive power. Neither paper gave any concrete complexity bound and the results in these papers are stated for subsets of solutions only, whereas our results concern all solutions.

On a Factorisation of Free Monoids

1965 ◽  
Vol 16 (1) ◽  
pp. 21 ◽  
Author(s):  
M. P. Schutzenberger
Keyword(s):  
Free Monoids

Reconstruction of protein and nucleic acid sequences: IV. The algebra of free monoids and the fragmentation stratagem

1966 ◽  
Vol 28 (2) ◽  
pp. 235-260 ◽  
Author(s):  
J. E. Mosimann ◽  
M. B. Shapiro ◽  
C. R. Merril ◽  
D. F. Bradley ◽  
J. E. Vinton
Keyword(s):  
Nucleic Acid ◽  
Free Monoids ◽  
Nucleic Acid Sequences

scholarly journals Congruences on free monoids and submonoids of polycyclic monoids

1993 ◽  
Vol 54 (2) ◽  
pp. 236-253 ◽  
Author(s):  
John Meakin ◽  
Mark Sapir
Keyword(s):  
Semigroup Theory ◽  
Free Monoid ◽  
Inverse Semigroups ◽  
Free Monoids ◽  
One To One

AbstractWe establish a one-to-one “group-like” correspondence between congruences on a free monoid X* and so-called positively self-conjugate inverse submonoids of the polycyclic monoid P(X). This enables us to translate many concepts in semigroup theory into the language of inverse semigroups.

Retracts of free monoids are nowhere dense with respect to finite group topologies and p-adic topologies

1991 ◽  
Vol 42 (1) ◽  
pp. 117-119 ◽  
Author(s):  
Wit Foryś ◽  
Tom Head
Keyword(s):  
Finite Group ◽  
Free Monoids

Factorizations of Free Monoids

1997 ◽  
pp. 63-104
Author(s):  
Perrin Dominique
Keyword(s):  
Free Monoids
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