Search results for "Hopcroft's algorithm"
showing 3 items of 3 documents
Hopcroft’s Algorithm and Cyclic Automata
2008
Minimization of deterministic finite automata is a largely studied problem of the Theory of Automata and Formal Languages. It consists in finding the unique (up to isomorphism) minimal deterministic automaton recognizing a set of words. The first approaches to this topic can be traced back to the 1950’s with the works of Huffman and Moore (cf. [12,15]). Over the years several methods to solve this problem have been proposed but the most efficient algorithm in the worst case was given by Hopcroft in [11]. Such an algorithm computes in O(n log n) the minimal automaton equivalent to a given automaton with n states. The Hopcroft’s algorithm has been widely studied, described and implemented by …
Hopcroft's algorithm and tree-like automata
2011
Minimizing a deterministic finite automata (DFA) is a very important problem in theory of automata and formal languages. Hopcroft's algorithm represents the fastest known solution to the such a problem. In this paper we analyze the behavior of this algorithm on a family binary automata, called tree-like automata, associated to binary labeled trees constructed by words. We prove that all the executions of the algorithm on tree-like automata associated to trees, constructed by standard words, have running time with the same asymptotic growth rate. In particular, we provide a lower and upper bound for the running time of the algorithm expressed in terms of combinatorial properties of the trees…
On Extremal Cases of Hopcroft’s Algorithm
2009
In this paper we consider the problem of minimization of deterministic finite automata (DFA) with reference to Hopcroft’s algorithm. Hopcroft’s algorithm has several degrees of freedom, so there can exist different sequences of refinements of the set of the states that lead to the final partition. We find an infinite family of binary automata for which such a process is unique. Some recent papers (cf. [3,7,1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata associated to circular words. However, automata minimization can be achieved also in linear time when the alphabet has only one letter (cf. [14]), so in …