Related papers: A combinatorial approach for the state complexity …
The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of…
Analysis of the process of accumulation of the results of measurements shows that the success of this process substantially depends on the possibility of coordination of actions of two participants of the process - preparator who prepares…
We generalize the shuffle theorem and its $(km,kn)$ version, as conjectured by Haglund et al. and Bergeron et al., and proven by Carlsson and Mellit, and Mellit, respectively. In our version the $(km,kn)$ Dyck paths on the combinatorial…
We resolve an open question by determining matching (asymptotic) upper and lower bounds on the state complexity of the operation that sends a language L to (c(L*))*, where c() denotes complement.
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited…
The shuffle product plays an important role in the study of multiple zeta values. This is expressed in terms of multiple integrals, and also as a product in a certain non-commutative polynomial algebra over the rationals in two…
In this paper, we introduce the new concept of state complexity approximation, which is a further development of state complexity estimation. We show that this new concept is useful in both of the following two cases: the exact state…
A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the…
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next…
Formal reasoning about distributed algorithms (like Consensus) typically requires to analyze global states in a traditional state-based style. This is in contrast to the traditional action-based reasoning of process calculi. Nevertheless,…
We show that the commutative closure combined with the iterated shuffle is a regularity-preserving operation on group languages. In particular, for commutative group languages, the iterated shuffle is a regularity-preserving operation. We…
We study the state complexity of binary operations on regular languages over different alphabets. It is known that if $L'_m$ and $L_n$ are languages of state complexities $m$ and $n$, respectively, and restricted to the same alphabet, the…
The notion of Online State Complexity, introduced by Karp in 1967, quantifies the amount of states required to solve a given problem using an online algorithm, which is represented by a deterministic machine scanning the input from left to…
We introduce "binding complexity", a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases the…