Related papers: On groups whose word problem is solved by a nested…
We show that the Word Problem in finitely generated subgroups of $\textsf{GL}_d(\mathbb{Z})$ can be solved in linear average-case complexity. This is done under the bit-complexity model, which accounts for the fact that large integers are…
We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre. We describe an…
Separability for groups refers to the question which subsets of a group can be detected in its finite quotients. Classically, separability is studied in terms of which classes have a certain separability property, and this question is…
An automaton is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis…
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…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change…
Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup.
History-deterministic automata are those in which nondeterministic choices can be correctly resolved stepwise: there is a strategy to select a continuation of a run given the next input letter so that if the overall input word admits some…
Motivated by the increasing interest in the explicit representation and handling of various "preference" structures arising in modern digital economy, this work introduces a new class of "one-to-many stable-matching" problems where a set of…
We study the satisfiability of string constraints where context-free membership constraints may be imposed on variables. Additionally a variable may be constrained to be a subword of a word obtained by shuffling variables and their…
We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with…
A saturation algorithm for collapsible pushdown systems was published in ICALP 2012. This work introduced a class of stack automata used to recognised regular sets of collapsible pushdown configurations. It was shown that these automata…
In this paper we investigate the word problem of the free Burnside semigroup satisfying x^2=x^3 and having two generators. Elements of this semigroup are classes of equivalent words. A natural way to solve the word problem is to select a…
We show that the class of finitely generated virtually free groups is precisely the class of demonstrable subgroups for R. Thompson's group $V$. The class of demonstrable groups for $V$ consists of all groups which can embed into $V$ with a…
Free Steiner triple systems (STS) are infinite structures that are naturally characterised by a universal property. We consider the class of free STSs from a model theoretic viewpoint. We show that free STSs on any number of generators are…
We describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the word problem in a topological full group is solvable if and only if the language of the underlying…
An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is k-ambiguous (for k > 0) if for every input it has at most k accepting computations. An automaton is boundedly ambiguous if it is…
We call the family of free-by-cyclic groups defined by $G = \left< a, t, b_1, b_2, \ldots b_k \mid at = ta, b_1^{-1}tb_1 = a^{n_1}t, \ldots b_k^{-1}tb_k = a^{n_k}t \right>$ for $n_1, n_2, \ldots n_k \in \mathbb Z$ linearly mismatched since…
The value 1 problem is a decision problem for probabilistic automata over finite words: are there words accepted by the automaton with arbitrarily high probability? Although undecidable, this problem attracted a lot of attention over the…