Implementation of the Hopcroft’s Algorithm
نویسنده
چکیده
Minimization of a deterministic finite automaton(DFA) is a well-studied problem of formal language. An efficient algorithm for this problem is proposed by Hopcroft in 1970 and we have already learned this algorithm in the course. The goal of this writing is to discuss how this algorithm is carried out in time complexity O(MNlog2N)(where M is the size of alphabet and N is the number of states). The writing is in three sections: first, we review the original algorithm; second, we provide corresponding data structures for carrying out the algorithm efficiently; and at last we prove that the algorithm is indeed in time O(MNlog2N) using these data structures.
منابع مشابه
Around Hopcroft's Algorithm
In this paper, a reflection is made on an indeterminism inherent to Hopcroft’s minimization algorithm: the splitter choice. We have implemented two natural policies (FIFO and FILO) for managing the set of splitters for which we obtain the following practical results: the FILO strategy performs better than the FIFO strategy, in the case of a one letter alphabet, the practical complexity in the F...
متن کاملContinuant polynomials and worst-case behavior of Hopcroft's minimization algorithm
This paper is concernedwith the analysis of theworst case behavior of Hopcroft’s algorithm for minimizing deterministic finite state automata. We extend a result of Castiglione, Restivo and Sciortino. They show that Hopcroft’s algorithm has a worst case behavior for the automata recognizing Fibonacci words. In a previous paper, we have proved that this holds for all standard Sturmian words havi...
متن کاملOn the Hopcroft's minimization algorithm
We show that the absolute worst case time complexity for Hopcroft’s minimization algorithm applied to unary languages is reached only for de Bruijn words. A previous paper by Berstel and Carton gave the example of de Bruijn words as a language that requires O(n log n) steps by carefully choosing the splitting sets and processing these sets in a FIFO mode. We refine the previous result by showin...
متن کاملManuel Baclet and Claire Pagetti Around Hopcroft ’ s Algorithm Research Report LSV - 06 - 12 May 2006
In this paper, a reflection is made on an indeterminism inherent to Hopcroft’s minimization algorithm: the splitter choice. We have implemented two natural policies (FIFO and FILO) for managing the set of splitters for which we obtain the following practical results: the FILO strategy performs better than the FIFO strategy, in the case of a one letter alphabet, the practical complexity in the F...
متن کاملHopcroft’s automaton minimization algorithm and Sturmian words
An algorithm for the minimization of deterministic finite state automata that runs in time O(n log n) on automata with n states was given by Hopcroft (1971). It is, up to now, the most efficient algorithm known in the general case. We address here the problem of showing that the running time O(n log n) for Hopcroft algorithms is tight. This algorithm has a degree of freedom because, in each ste...
متن کاملExperimental Evaluation of Classical Automata Constructions
There are several algorithms for producing the canonical DFA from a given NFA. While the theoretical complexities of these algorithms are known, there has not been a systematic empirical comparison between them. In this work we propose a probabilistic framework for testing the performance of automatatheoretic algorithms. We conduct a direct experimental comparison between Hopcroft’s and Brzozow...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009