Related papers: An Improved Algorithm for Finding the Shortest Syn…
The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond…
Most slowly synchronizing automata over binary alphabets are circular, i.e., containing a letter permuting the states in a single cycle, and their set of synchronizing words has maximal state complexity, which also implies complete…
We study synchronizing automata with the shortest reset words of relatively large length. First, we refine the Frankl-Pin result on the length of the shortest words of rank $m$, and the B\'eal, Berlinkov, Perrin, and Steinberg results on…
Instead of looking at the lengths of synchronizing words as in \v{C}ern\'y's conjecture, we look at the switch count of such words, that is, we only count the switches from one letter to another. Where the synchronizing words of the…
Synchronizing words in classical automata theory provide a mechanism to reset any state of a deterministic automaton to a specific target state via a carefully chosen finite sequence of transition rules. In this work, we extend the concept…
The {\em asynchronous automaton} associated with a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$, considered in many applications, is the finite deterministic automaton where the set of states is $\{0,1\}^n$, the alphabet is $[n]$, and the…
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 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…
We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\varTheta(n^2)$, where…
A goal of this paper is to introduce the new construction of an automaton with shortest synchronizing word of length $O(d^{\frac{n}{d}})$, where $d \in \mathbb{N}$ and $n$ is the number of states for that automaton. Additionally we…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
In this report we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic Buchi, Co-Buchi, and parity…
We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This…
We consider the first problem that appears in any application of synchronizing automata, namely, the problem of deciding whether or not a given $n$-state $k$-letter automaton is synchronizing. First we generalize results from…
String matching is the problem of finding all the occurrences of a pattern in a text. We propose improved versions of the fast family of string matching algorithms based on hashing $q$-grams. The improvement consists of considering minimal…
This paper considers the existence of short synchronizing words in deterministic finite automata (DFAs). We define two general strategies for generating synchronizing words, and we show that each of these strategies can be applied if and…
String matching is the problem of finding all the substrings of a text which match a given pattern. It is one of the most investigated problems in computer science, mainly due to its very diverse applications in several fields. Recently,…
Using combinatorial properties of incomplete sets in a free monoid we construct a series of n-state deterministic automata with zero whose shortest synchronizing word has length n^2/4+n/2-1.
A word w of letters on edges of underlying graph Gamma of deterministic finite automaton (DFA) is called the synchronizing word if w sends all states of the automaton to a unique state. J. Cerny discovered in 1964 a sequence of n-state…
We consider the problem {\sc Max Sync Set} of finding a maximum synchronizing set of states in a given automaton. We show that the decision version of this problem is PSPACE-complete and investigate the approximability of {\sc Max Sync Set}…