相关论文: Asymptotic enumeration of Minimal Automata
We give an exact enumerative formula for the minimal acyclic deterministic finite automata. This formula is obtained from a bijection between a family of generalized parking functions and the transitions functions of acyclic automata.
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…
We investigate finite deterministic automata in sets with non-homogeneous atoms: integers with successor. As there are uncount- ably many deterministic finite automata in this setting, we restrict our attention to automata with semilinear…
Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits. It is proved that if two sets of numbers S and T are represented by…
In this paper we address the question of synchronizing random automata in the critical settings of almost-group automata. Group automata are automata where all letters act as permutations on the set of states, and they are not synchronizing…
We give an unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFAs) with n states over an alphabet of k symbols. We show how to generate all these strings for each n and k, and how its…
In the classical theory of formal languages, finite state automata allow to recognize the words of a rational subset of $\Sigma^*$ where $\Sigma$ is a set of symbols (or the alphabet). Now, given a semiring $(\K,+,.)$, one can construct…
In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite-state automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it.…
The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random $n$-state DFAs over a $k$-symbol alphabet, drawn uniformly from the set…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a…
A deterministic finite (semi)automaton is primitive if its transition monoid (semigroup) acting on the set of states has no non-trivial congruences. It is synchronizing if it contains a constant map (transformation). In analogy to…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
We generalize the partial derivative automaton to regular expressions with shuffle and study its size in the worst and in the average case. The number of states of the partial derivative automata is in the worst case at most 2^m, where m is…
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.
A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…
A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. It was conjectured that in each completely…
We introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the `canonical boolean representation' of the syntactic monoid. Equivalently, it is the least number of…
Given a member A of the class of non-deterministic timed automata with silent transitions (eNTA), we effectively compute its timestamp: the set of all pairs (time value, action) of all observable timed traces of A, a generalization of the…
In this paper, we first introduce a lower bound technique for the state complexity of transformations of automata. Namely we suggest first considering the class of full automata in lower bound analysis, and later reducing the size of the…