Related papers: The Complexity of Finding Reset Words in Finite Au…
We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that…
Register pushdown automata (RPDA) is an extension of classical pushdown automata to handle data values in a restricted way. RPDA attracts attention as a model of a query language for structured documents with data values. The membership and…
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…
In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is…
In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we show that a more general version of the finiteness problem…
We generalize the concept of synchronizing words for finite automata, which map all states of the automata to the same state, to deterministic visibly push-down automata. Here, a synchronizing word w does not only map all states to the same…
We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
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…
Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
Given a finite alphabet $\Sigma$ and a deterministic finite automaton on $\Sigma$, the problem of determining whether the language recognized by the automaton contains any pangram is \NP-complete. Various other language classes and problems…
We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists a word contained in their…
We present a new heuristic algorithm finding reset words. The algorithm called CutOff-IBFS is based on a simple idea of inverse breadth-first-search in the power automaton. We perform an experimental investigation of effectiveness compared…
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…
In this paper, we study the problem of determining a minimum state probabilistic finite state machine capable of generating statistically identical symbol sequences to samples provided. This problem is qualitatively similar to the classical…
We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…