Related papers: Knapsack problem for automaton groups
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 problem of constructing matched groups such that the resulting groups are statistically similar with respect to their average values for multiple covariates. This group-matching problem arises in many cases, including…
In this paper, we study some multiagent variants of the knapsack problem. Fluschnik et al. [AAAI 2019] considered the model in which every agent assigns some utility to every item. They studied three preference aggregation rules for finding…
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the…
In this paper we introduce the Ameso optimization problem, a special class of discrete optimization problems. We establish its basic properties and investigate the relation between Ameso optimization and the convex optimization. Further, we…
We solve some decision problems for timed automata which were recently raised by S. Tripakis in [ Folk Theorems on the Determinization and Minimization of Timed Automata, in the Proceedings of the International Workshop FORMATS'2003, LNCS,…
We prove new complexity results for computational problems in certain wreath products of groups and (as an application) for free solvable group. For a finitely generated group we study the so-called power word problem (does a given…
In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to…
Stallings folding theory is modified, using double coset representatives, and to applied to the study of subgroups of amalgamated products of finite rank free groups. As a first application the subgroup membership problem for such groups is…
We consider decidability problems in self-similar semigroups, and in particular in semigroups of automatic transformations of $X^*$. We describe algorithms answering the word problem, and bound its complexity under some additional…
The conjugacy problem for a finitely generated group $G$ is the two-variable problem of deciding for an arbitrary pair $(u,v)$ of elements of $G$, whether or not $u$ is conjugate to $v$ in $G$. We construct examples of finitely generated,…
We establish a classification of decision problems that are to be solved by mobile agents operating in unlabeled graphs, using a deterministic protocol. The classification is with respect to the ability of a team of agents to solve the…
Stackability for finitely presented groups consists of a dynamical system that iteratively moves paths into a maximal tree in the Cayley graph. Combining with formal language theoretic restrictions yields auto- or algorithmic stackability,…
Autostackability for finitely presented groups is a topological property of the Cayley graph combined with formal language theoretic restrictions, that implies solvability of the word problem. The class of autostackable groups is known to…
We study the conjugacy problem in the automorphism group $Aut(T)$ of a regular rooted tree $T$ and in its subgroup $FAut(T)$ of finite-state automorphisms. We show that under the contracting condition and the finiteness of what we call the…
In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…
In the 1980's Stallings showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…