Deterministic Finite Cover Automata Research Articles

Two Extensions of Cover Automata

Deterministic Finite Cover Automata (DFCA) are compact representations of finite languages. Deterministic Finite Automata with “do not care” symbols and Multiple Entry Deterministic Finite Automata are both compact representations of regular languages. This paper studies the benefits of combining these representations to get even more compact representations of finite languages. DFCAs are extended by accepting either “do not care” symbols or considering multiple entry DFCAs. We study for each of the two models the existence of the minimization or simplification algorithms and their computational complexity, the state complexity of these representations compared with other representations of the same language, and the bounds for state complexity in case we perform a representation transformation. Minimization for both models proves to be NP-hard. A method is presented to transform minimization algorithms for deterministic automata into simplification algorithms applicable to these extended models. DFCAs with “do not care” symbols prove to have comparable state complexity as Nondeterministic Finite Cover Automata. Furthermore, for multiple entry DFCAs, we can have a tight estimate of the state complexity of the transformation into equivalent DFCA.

Simplifying Nondeterministic Finite Cover Automata

The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA '98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language, Nondeterministic Finite Automata (NFA) may significantly reduce the number of states used. The combined power of the succinctness of the representation of finite languages using both cover languages and non-determinism has been suggested, but never systematically studied. In the present paper, for nondeterministic finite cover automata (NFCA) and l-nondeterministic finite cover automaton (l-NFCA), we show that minimization can be as hard as minimizing NFAs for regular languages, even in the case of NFCAs using unary alphabets. Moreover, we show how we can adapt the methods used to reduce, or minimize the size of NFAs/DFCAs/l-DFCAs, for simplifying NFCAs/l-NFCAs.

Learning finite cover automata from queries

Learning regular languages from queries was introduced by Angluin in a seminal paper that also provides the L ⁎ algorithm. This algorithm, as well as other existing inference methods, finds the exact language accepted by the automaton. However, when only finite languages are used, the construction of a deterministic finite cover automaton ( DFCA) is sufficient. A DFCA of a finite language U is a finite automaton that accepts all sequences in U and possibly other sequences that are longer than any sequence in U. This paper presents an algorithm, called L l , that finds a minimal DFCA of an unknown finite language in polynomial time using membership and language queries, a non-trivial adaptation of Angluinʼs L ⁎ algorithm. As the size of a minimal DFCA of a finite language U may be much smaller than the size of the minimal automaton that accepts exactly U, L l can provide substantial savings over existing automata inference methods.

HYPER-MINIMIZATION IN O(n2)

Two formal languages are f-equivalent if their symmetric difference L1 Δ L2 is a finite set — that is, if they differ on only finitely many words. The study of f -equivalent languages, and particularly the DFAs that accept them, was recently introduced [3]. First, we restate the fundamental results in this new area of research. Second, we introduce our main result, which is a faster algorithm for the natural minimization problem: given a starting DFA D, find the smallest (by number of states) DFA D′ such that L(D) and L(D′) are f -equivalent. Finally, we suggest a technique that combines this hyper-minimization with the well-studied notion of a deterministic finite cover automaton [2, 4, 5], or DFCA, thereby extending the applicability of DFCAs from finite to infinite regular languages.

Finite state based testing of P systems

In this paper, we propose an approach to P system testing based on finite state machine conformance techniques. Of the many variants of P systems that have been defined, we consider cell-like P systems which use non-cooperative transformation and communication rules. We show that a (minimal) deterministic finite cover automaton (DFCA) (a finite automaton that accepts all words in a given finite language, but can also accept words that are longer than any word in the language) provides the right approximation for the computation of a P system. Furthermore, we provide a procedure for generating test sets directly from the P system specification (without explicitly constructing the minimal DFCA model).

Incremental construction of minimal deterministic finite cover automata

We present a fast incremental algorithm for constructing minimal Deterministic Finite Cover Automata (DFCA) for a given language. Since it was shown that the minimal DFCA for a language L has less states than the minimal Deterministic Finite Automata (DFA) for the same language L, this technique seems to be the best choice for incrementally building the automaton for a large language, especially when the number of states in the DFCA is significantly less than the number of states in the corresponding minimal DFA. We have implemented the proposed algorithm and have tested it against the best-known DFCA minimization technique.

Results on Transforming NFA into DFCA

In this paper we consider the transformation from (minimal) non-deterministic finite automata (NFAs) to deterministic finite cover automata (DFCAs). We want to compare the two equivalent accepting ...

AN EFFICIENT ALGORITHM FOR CONSTRUCTING MINIMAL COVER AUTOMATA FOR FINITE LANGUAGES

The concept of cover automata for finite languages was formally introduced in [3]. Cover automata have been studied as an efficient representation of finite languages. In [3], an algorithm was given to transform a DFA that accepts a finite language to a minimal deterministic finite cover automaton (DFCA) with the time complexity O(n4), where n is the number of states of the given DFA. In this paper, we review the basic concept of cover automata and describe a new efficient transformation algorithm with the time complexity O(n2), which is a significant improvement from the previous algorithm.

Minimal cover-automata for finite languages

A cover-automaton A of a finite language L⊆Σ ∗ is a finite deterministic automaton (DFA) that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic finite cover automaton (DFCA) of a finite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of finite languages in practice. In this paper, we describe an efficient algorithm that, for a given DFA accepting a finite language, constructs a minimal deterministic finite cover-automaton of the language. We also give algorithms for the boolean operations on deterministic cover automata, i.e., on the finite languages they represent.