Related papers: The Intersection Problem for Finite Monoids
The notion of delays arises naturally in many computational models, such as, in the design of circuits, control systems, and dataflow languages. In this work, we introduce \emph{automata with delay blocks} (ADBs), extending finite state…
The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…
Genome rearrangements are events in which large blocks of DNA exchange pieces during evolution. The analysis of such events is a tool for understanding evolutionary genomics, based on finding the minimum number of rearrangements to…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
We prove that the word problem of a finitely generated group $G$ is in NP (solvable in polynomial time by a non-deterministic Turing machine) if and only if this group is a subgroup of a finitely presented group $H$ with polynomial…
We analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et…
The NP-complete Permutation Pattern Matching problem asks whether a permutation P (the pattern) can be matched into a permutation T (the text). A matching is an order-preserving embedding of P into T. In the Generalized Permutation Pattern…
Matroid is a generalization of many fundamental objects in combinatorial mathematics , and matroid intersection problem is a classical subject in combinatorial optimization . However , only the intersection of two matroids are well…
We present a definition of the class NP in combinatorial context as the set of languages of structures defined by finitely many forbidden lifted substructures. We apply this to special syntactically defined subclasses and show how they…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
We show that the compressed word problem in a finitely-generated fully residually free group (F -group) is decidable in polynomial time, and use the result to show that the word problem in the automorphism group of such a group is decidable…
We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight line programs defined…
There has been a significant interest in extending various modal logics with intersection, the most prominent examples being epistemic and doxastic logics with distributed knowledge. Completeness proofs for such logics tend to be…
It is known how to compute the Zariski closure of a finitely generated monoid of matrices and, more generally, of a set of matrices specified by a regular language. This result was recently used to give a procedure to compute all polynomial…
We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that…
Zimin words are very special finite words which are closely related to the pattern-avoidability problem. This problem consists in testing if an instance of a given pattern with variables occurs in almost all words over any finite alphabet.…
In this note we study automata recognizing birecurrent sets. A set of words is birecurrent if the minimal partial DFA recognizing this set and the minimal partial DFA recognizing the reversal of this set are both strongly connected. This…
In this paper we examine decision problems associated with various classes of convex languages, studied by Ang and Brzozowski (under the name "continuous languages"). We show that we can decide whether a given language L is prefix-,…
We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the…