Related papers: Solutions to twisted word equations and equations …
It is proved that the periodic point submonoid of a free inverse monoid endomorphism is always finitely generated. Using Chomsky's hierarchy of languages, we prove that the fixed point submonoid of an endomorphism of a free inverse monoid…
We give a simple algorithm to solve the subgroup membership problem for virtually free groups. For a fixed virtually free group with a fixed generating set $X$, the subgroup membership problem is uniformly solvable in time $O(n\log^*(n))$…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages~$L$ that assign to each word~$w$ a real number~$L(w)$. In the case of infinite words, the value of a run is…
We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of…
This paper present several refinements of the Datalog +/- framework based on resolution and Datalog-rewriting. We first present a resolution algorithm which is complete for arbitrary sets of tgds and egds. We then show that a technique of…
The Toroidal Lie algebras are n variable genaralizations of Affine Kac-Moody Lie algebras. As in the affine Lie algebras there exists finite order auto= morphisms corresponding to Dynkin diagram automorphisms. The fixed point sub= algebras…
We generalize the classical definition of effectively closed subshift to finitely generated groups. We study classical stability properties of this class and then extend this notion by allowing the usage of an oracle to the word problem of…
We continue our investigation of a variation of the group ring isomorphism problem for twisted group algebras. Contrary to previous work, we include cohomology classes which do not contain any cocycle of finite order. This allows us to…
In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Here, we investigate weighted context-free languages of infinite words, a generalization of $\omega$-context-free…
We prove that every finitely generated, virtually solvable minimax group can be expressed as a homomorphic image of a virtually torsion-free, virtually solvable minimax group. This result enables us to generalize a theorem of Ch. Pittet and…
We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we demonstrate a context-free…
We prove that in every finitely generated profinite group, every subgroup of finite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is deduced from the main result about finite…
In this work we investigate tensor completions of groups by associative rings, which were introduced by R.Lyndon and G.Baumslag in 1960s. The main result states that there exists an algorithm that decides if a given finite system of…
One of the most interesting questions about a group is if its word problem can be solved and how. The word problem in the braid group is of particular interest to topologists, algebraists and geometers, and is the target of intensive…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages $L$ that assign to each word $w$ a real number $L(w)$. In the case of infinite words, the value of a run is…
A systematic construction of a class of integrable hierarchy is discussed in terms of the twisted affine $A_{2r}^{(2)}$ Lie algebra. The zero curvature representation of the time evolution equations are shown to be classified according to…
The Petrov solution (for $\Lambda=0$) and the Kaigorodov-Ozsv\'ath solution (for $\Lambda<0$) provide examples of vacuum solutions of the Einstein equations with simply-transitive isometry groups. We calculate the boundary stress-tensor for…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
Let $\Gamma$ be a Coxeter graph, let $(W,S)$ be its associated Coxeter system, and let $(A,\Sigma$) be its associated Artin-Tits system. We regard $W$ as a reflection group acting on a real vector space $V$. Let $I$ be the Tits cone, and…
The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…