Related papers: Undecidable word problem in subshift automorphism …
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
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…
It is shown that the compressed word problem for an HNN-extension with base group H and finite associated subgroups is polynomial time Turing-reducible to the compressed word problem for H. An analogous result for amalgamated free products…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
The complexity and decidability of various decision problems involving the shuffle operation are studied. The following three problems are all shown to be $NP$-complete: given a nondeterministic finite automaton (NFA) $M$, and two words $u$…
For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…
Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing…
Given an infinite linear group with a finite set of generators, we show that the shortest word length of an element of infinite order has an upper bound that depends only on the number of generators and the degree. This provides a…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
Let F_2 denote the free group of rank 2. Our main technical result of independent interest is: for any element u of F_2, there is g in F_2 such that no cyclically reduced image of u under an automorphism of F_2 contains g as a subword. We…
A word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state. Deciding about the existence of a reset word of a given maximum length for a given automaton is known to be an…
We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [4] and generalizes the result of [2].
The determinisation problem for min-plus (tropical) weighted automata was recently shown to be decidable. However, the proof is purely existential, relying on several non-constructive arguments. Our contribution in this work is twofold:…
We study finite subgroups of outer automorphisms of free products. We give upper bounds for the orders of these finite subgroups as well as bounds for the orders of individual torsion outer automorphisms under some (necessary) conditions…
We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and…
We study the interrelation of space functions of groups and the space complexity of the algorithmic word problem in groups.
The subword complexity of a word $w$ over a finite alphabet $\mathcal{A}$ is a function that assigns for each positive integer $n$, the number of distinct subwords of length $n$ in $w$. The subword complexity of a word is a good measure of…
This paper presents a mechanism of resolving unidentified lexical units in Text-based Machine Translation (TBMT). In a Machine Translation (MT) system it is unlikely to have a complete lexicon and hence there is intense need of a new…
We determine the structure of automorphism group or each nonsplit metacyclic 2-group. This completes the work on automorphism groups of metacyclic $p$-groups.
We study decision problems of the form: given a regular or linear context-free language $L$, is there a word of a given fixed form in $L$, where given fixed forms are based on word operations copy, marked copy, shuffle and their…