Related papers: Matrix approach to synchronizing automata
In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…
For general input automata, there exist regular constraint languages such that asking if a given input automaton admits a synchronizing word in the constraint language is PSPACE-complete or NP-complete. Here, we investigate this problem for…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
Given a regular language L over an ordered alphabet $\Sigma$, the set of lexicographically smallest (resp., largest) words of each length is itself regular. Moreover, there exists an unambiguous finite-state transducer that, on a given word…
We develop a fully diagrammatic approach to the theory of finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. Moreover, we provide an…
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…
The asynchronous dynamics associated with a Boolean network $f : \{0,1\}^n \to \{0,1\}^n$ is a finite deterministic automaton considered in many applications. The set of states is $\{0,1\}^n$, the alphabet is $[n]$, and the action of letter…
Previously, self-verifying symmetric difference automata were defined and a tight bound of 2^n-1-1 was shown for state complexity in the unary case. We now consider the non-unary case and show that, for every n at least 2, there is a…
The identification of a deterministic finite automaton (DFA) from labeled examples is a well-studied problem in the literature; however, prior work focuses on the identification of monolithic DFAs. Although monolithic DFAs provide accurate…
In general, the representation of combinatorial objects is decisive for the feasibility of several enumerative tasks. In this work, we show how a (unique) string representation for (complete) initially-connected deterministic automata…
A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…
We tackle the problem of the randomized generation of slowly synchronizing deterministic automata (DFAs) by generating random primitive sets of matrices. We show that when the randomized procedure is too simple the exponent of the generated…
Bernard Lang defines parsing as the calculation of the intersection of a FSA (the input) and a CFG. Viewing the input for parsing as a FSA rather than as a string combines well with some approaches in speech understanding systems, in which…
We provide the first fully polynomial-time randomized approximation scheme for the following two counting problems: 1. Given a Context Free Grammar $G$ over alphabet $\Sigma$, count the number of words of length exactly $n$ generated by…
Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract…
We present a polynomial time algorithm that constructs a deterministic parity automaton (DPA) from a given set of positive and negative ultimately periodic example words. We show that this algorithm is complete for the class of…
Matching statistics were introduced to solve the approximate string matching problem, which is a recurrent subroutine in bioinformatics applications. In 2010, Ohlebusch et al. [SPIRE 2010] proposed a time and space efficient algorithm for…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…