Related papers: On the Word Problem for Compressible Monoids
We study the language-theoretic aspects of the word problem, in the sense of Duncan & Gilman, of free products of semigroups and monoids. First, we provide algebraic tools for studying classes of languages known as super-AFLs, which…
A monoid is called special if it admits a presentation in which all defining relations are of the form $w = 1$. Every group is special, but not every monoid is special. In this article, we describe the language-theoretic properties of the…
The compressed word problem for a finitely generated monoid M asks whether two given compressed words over the generators of M represent the same element of M. For string compression, straight-line programs, i.e., context-free grammars that…
We study subsets of groups and monoids defined by language-theoretic means, generalizing the classical approach to the word problem. We expand on results by Herbst from 1991 to a more general setting, and for a class of languages…
This paper considers the word problem for free inverse monoids of finite rank from a language theory perspective. It is shown that no free inverse monoid has context-free word problem; that the word problem of the free inverse monoid of…
A special inverse monoid is one defined by a presentation where all the defining relations have the form $r = 1$. By a result of Ivanov Margolis and Meakin the word problem for such an inverse monoid can often be reduced to the word problem…
We show that any finite monoid or semigroup presentation satisfying the small overlap condition C(4) has word problem which is a deterministic rational relation. It follows that the set of lexicographically minimal words forms a regular…
We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through…
We prove the following results: (1) There is a one-relator inverse monoid $\mathrm{Inv}\langle A\:|\:w=1 \rangle$ with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The first…
We study a class of inverse monoids of the form M = Inv< X | w=1 >, where the single relator w has a combinatorial property that we call sparse. For a sparse word w, we prove that the word problem for M is decidable. We also show that the…
We show that the compressed word problem in a finitely-generated fully residually free group (F -group) is decidable in polynomial time, and use the result to show that the word problem in the automorphism group of such a group is decidable…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
Motivated by the question of which completely regular semigroups have context-free word problem, we show that for certain classes of languages $\mathfrak{C}$(including context-free), every completely regular semigroup that is a union of…
The Diophantine problem for a monoid $M$ is the decision problem to decide whether any given system of equations has a solution in $M$. In this note, we give a simple example of a context-free, word-hyperbolic, finitely presented, special…
This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the…
In this paper we prove several results regarding decidability of the membership problem for certain submonoids in amalgamated free products and HNN extensions of groups. These general results are then applied to solve the prefix membership…
The \emph{word problem} of a group $G = \langle \Sigma \rangle$ can be defined as the set of formal words in $\Sigma^*$ that represent the identity in $G$. When viewed as formal languages, this gives a strong connection between classes of…
We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class…
We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free…
Anisimov and Seifert show that a group has a regular word problem ifand only if it is finite. Muller and Schupp (together with Dunwoody's accessibility result) show that a group has context free word problem if and only if it is virtually…