Related papers: Rational semigroup automata
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…
Commutative languages with the semilinear property (SLIP) can be naturally recognized by real-time NLOG-SPACE multi-counter machines. We show that unions and concatenations of such languages can be similarly recognized, relying on -- and…
We study the globalization problem for a strong partial action $\alpha$ of a monoid $M$ on a semigroup $X$ via the associated rewriting system $(X_M^+,\to)$. We show that the local confluence of $(X_M^+,\to)$ is sufficient for the…
It is shown that for every language family that is a trio containing only semilinear languages, all bounded languages in it can be accepted by one-way deterministic reversal-bounded multicounter machines (DCM). This implies that for every…
We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma…
A Wheeler automaton is a finite state automaton whose states admit a total Wheeler order, reflecting the co-lexicographic order of the strings labeling source-to-node paths. A Wheeler language is a regular language admitting an accepting…
We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zero-simple semigroups for which…
Let A be a finite alphabet and let L contained in (A*)^n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an…
The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L' are binary regular languages with quotient complexities m and n, and that the…
The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics---languages over an…
With each semigroup one can associate a partial algebra, called the biordered set, which captures important algebraic and geometric features of the structure of idempotents of that semigroup. For a biordered set $\mathcal{E}$, one can…
Let W~ be an affine Weyl group, and let C be a left, right, or two-sided Kazhdan--Lusztig cell in W~. Let Reduced (C) be the set of all reduced expressions of elements of C, regarded as a formal language in the sense of the theory of…
A new class of languages of infinite words is introduced, called the max-regular languages, extending the class of $\omega$-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter…
We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of…
We prove that it is decidable whether or not a finitely generated submonoid of a virtually free group is graded, introduce a new geometric characterization as quasi-geodesic monoids, and show that their word problem is rational (as a…
The category of all idempotent generated semigroups with a prescribed structure $\mathcal{E}$ of their idempotents $E$ (called the biordered set) has an initial object called the free idempotent generated semigroup over $\mathcal{E}$,…
We study the complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids. We present polynomial time (quadratic in the RAM model of computation) algorithms to solve the word problem and…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the…
The starting point of algebraic language theory is that regular languages of finite words are exactly those recognized by finite monoids. This finiteness condition gives rise to a topological space whose points, called profinite words,…