An efficient incremental DFA minimization algorithm

2003 ◽  
Vol 9 (1) ◽  
pp. 49-64 ◽  
Author(s):  
BRUCE W. WATSON ◽  
JAN DACIUK
Keyword(s):  
Large Class ◽  
Finite Automata ◽  
Time Algorithm ◽  
The Other ◽  
Minimization Algorithm ◽  
Worst Case ◽  
Deterministic Finite Automata ◽  
Running Time ◽  
The Third ◽  
Minimization Algorithms

In this paper, we present a new Deterministic Finite Automata (DFA) minimization algorithm. The algorithm is incremental – it may be halted at any time, yielding a partially-minimized automaton. All of the other (known) minimization algorithms have intermediate results which are not useable for partial minimization. Since the first algorithm is easily understood but inefficient, we consider three practical and effective optimizations. The first two optimizations do not affect the asymptotic worst-case running time – though they perform well on a large class of automata. The third optimization yields an quadratic-time algorithm which is competitive with the previously known ones.

Space-bounded OTMs and REG ∞

Computability ◽  
2021 ◽  
pp. 1-16
Author(s):  
Merlin Carl
Keyword(s):  
Complexity Theory ◽  
Turing Machine ◽  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Finite Automata ◽  
Logarithmic Space ◽  
Working Space ◽  
Important Theorem

An important theorem in classical complexity theory is that REG = LOGLOGSPACE, i.e., that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs) and show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA, which is a transfinite analogue of LOGLOGSPACE ⊆ REG; the other direction, however, is easily seen to fail.

THE EDIT-DISTANCE BETWEEN A REGULAR LANGUAGE AND A CONTEXT-FREE LANGUAGE

2013 ◽  
Vol 24 (07) ◽  
pp. 1067-1082 ◽  
Author(s):  
YO-SUB HAN ◽  
SANG-KI KO ◽  
KAI SALOMAA
Keyword(s):  
Regular Language ◽  
Edit Distance ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The Other ◽  
Optimal Alignment ◽  
Worst Case ◽  
Context Free Language ◽  
Context Free ◽  
Free Language

The edit-distance between two strings is the smallest number of operations required to transform one string into the other. The distance between languages L1and L2is the smallest edit-distance between string wi∈ Li, i = 1, 2. We consider the problem of computing the edit-distance of a given regular language and a given context-free language. First, we present an algorithm that finds for the languages an optimal alignment, that is, a sequence of edit operations that transforms a string in one language to a string in the other. The length of the optimal alignment, in the worst case, is exponential in the size of the given grammar and finite automaton. Then, we investigate the problem of computing only the edit-distance of the languages without explicitly producing an optimal alignment. We design a polynomial time algorithm that calculates the edit-distance based on unary homomorphisms.

scholarly journals EFFICIENT DETERMINISTIC FINITE AUTOMATA SPLIT-MINIMIZATION DERIVED FROM BRZOZOWSKI'S ALGORITHM

2014 ◽  
Vol 25 (06) ◽  
pp. 679-696 ◽  
Author(s):  
PEDRO GARCÍA ◽  
DAMIÁN LÓPEZ ◽  
MANUEL VÁZQUEZ DE PARGA
Keyword(s):  
Computer Science ◽  
Finite Automata ◽  
Minimization Method ◽  
Deterministic Finite Automata ◽  
Classic Problem ◽  
Minimization Methods ◽  
Minimization Algorithms

Minimization of deterministic finite automata is a classic problem in Computer Science which is still studied nowadays. In this paper, we relate the different split-minimization methods proposed to date, or to be proposed, and the algorithm due to Brzozowski which has been usually set aside in any classification of DFA minimization algorithms. In our work, we first propose a polynomial minimization method derived from a paper by Champarnaud et al. We also show how the consideration of some efficiency improvements on this algorithm lead to obtain an algorithm similar to Hopcroft's classic algorithm. The results obtained lead us to propose a characterization of the set of possible splitters.

UNWEIGHTED AND WEIGHTED HYPER-MINIMIZATION

2012 ◽  
Vol 23 (06) ◽  
pp. 1207-1225 ◽  
Author(s):  
ANDREAS MALETTI ◽  
DANIEL QUERNHEIM
Keyword(s):  
Finite Automata ◽  
Reduction Technique ◽  
Regular Languages ◽  
Minimization Algorithm ◽  
Compression Method ◽  
Closure Properties ◽  
State Reduction ◽  
Deterministic Finite Automata ◽  
Input Strings ◽  
Weighted Finite Automata

Hyper-minimization of deterministic finite automata (DFA) is a recently introduced state reduction technique that allows a finite change in the recognized language. A generalization of this lossy compression method to the weighted setting over semifields is presented, which allows the recognized weighted language to differ for finitely many input strings. First, the structure of hyper-minimal deterministic weighted finite automata is characterized in a similar way as in classical weighted minimization and unweighted hyper-minimization. Second, an efficient hyper-minimization algorithm, which runs in time [Formula: see text], is derived from this characterization. Third, the closure properties of canonical regular languages, which are languages recognized by hyper-minimal DFA, are investigated. Finally, some recent results in the area of hyper-minimization are recalled.

scholarly journals Reversible parallel communicating finite automata systems

2021 ◽  
Vol 58 (4) ◽  
pp. 263-279
Author(s):  
Henning Bordihn ◽  
György Vaszil
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Case ◽  
Computational Power ◽  
Deterministic Finite Automata ◽  
Relationship Of ◽  
The Relationship ◽  
Context Free

AbstractWe study the concept of reversibility in connection with parallel communicating systems of finite automata (PCFA in short). We define the notion of reversibility in the case of PCFA (also covering the non-deterministic case) and discuss the relationship of the reversibility of the systems and the reversibility of its components. We show that a system can be reversible with non-reversible components, and the other way around, the reversibility of the components does not necessarily imply the reversibility of the system as a whole. We also investigate the computational power of deterministic centralized reversible PCFA. We show that these very simple types of PCFA (returning or non-returning) can recognize regular languages which cannot be accepted by reversible (deterministic) finite automata, and that they can even accept languages that are not context-free. We also separate the deterministic and non-deterministic variants in the case of systems with non-returning communication. We show that there are languages accepted by non-deterministic centralized PCFA, which cannot be recognized by any deterministic variant of the same type.

FROM C-CONTINUATIONS TO NEW QUADRATIC ALGORITHMS FOR AUTOMATON SYNTHESIS

2001 ◽  
Vol 11 (06) ◽  
pp. 707-735 ◽  
Author(s):  
J.-M. CHAMPARNAUD ◽  
D. ZIADI
Keyword(s):  
Time Complexity ◽  
Regular Expression ◽  
Time Algorithm ◽  
The Other ◽  
Worst Case ◽  
Partial Derivatives ◽  
Space And Time ◽  
Other Hand ◽  
Deterministic Automata ◽  
The Way

Two classical non-deterministic automata recognize the language denoted by a regular expression: the position automaton which deduces from the position sets defined by Glushkov and McNaughton–Yamada, and the equation automaton which can be computed via Mirkin's prebases or Antimirov's partial derivatives. Let |E| be the size of the expression and ‖E‖ be its alphabetic width, i.e. the number of symbol occurrences. The number of states in the equation automaton is less than or equal to the number of states in the position automaton, which is equal to ‖E‖+1. On the other hand, the worst-case time complexity of Antimirov algorithm is O(‖E‖3· |E|2), while it is only O(‖E‖·|E|) for the most efficient implementations yielding the position automaton (Brüggemann–Klein, Chang and Paige, Champarnaud et al.). We present an O(|E|2) space and time algorithm to compute the equation automaton. It is based on the notion of canonical derivative which makes it possible to efficiently handle sets of word derivatives. By the way, canonical derivatives also lead to a new O(|E|2) space and time algorithm to construct the position automaton.

scholarly journals A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set

2012 ◽  
Vol Vol. 14 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Serge Gaspers ◽  
Mathieu Liedloff
Keyword(s):  
Dominating Set ◽  
Independent Set ◽  
Time Algorithm ◽  
Worst Case ◽  
Running Time ◽  
Running Time Analysis ◽  
Np Hard Problem ◽  
International Audience ◽  
Maximal Independent Sets ◽  
Independent Dominating Set

Graphs and Algorithms International audience An independent dominating set D of a graph G = (V,E) is a subset of vertices such that every vertex in V \ D has at least one neighbor in D and D is an independent set, i.e. no two vertices of D are adjacent in G. Finding a minimum independent dominating set in a graph is an NP-hard problem. Whereas it is hard to cope with this problem using parameterized and approximation algorithms, there is a simple exact O(1.4423^n)-time algorithm solving the problem by enumerating all maximal independent sets. In this paper we improve the latter result, providing the first non trivial algorithm computing a minimum independent dominating set of a graph in time O(1.3569^n). Furthermore, we give a lower bound of \Omega(1.3247^n) on the worst-case running time of this algorithm, showing that the running time analysis is almost tight.

Complexities of Some Problems Related to Synchronizing, Non-Synchronizing and Monotonic Automata

2015 ◽  
Vol 26 (01) ◽  
pp. 99-121 ◽  
Author(s):  
Uraz Cengiz Türker ◽  
Hüsnü Yenigün
Keyword(s):  
Finite Automata ◽  
The Other ◽  
Np Hard ◽  
Deterministic Finite Automata ◽  
Practical Applications ◽  
Other Hand ◽  
Synchronizable Automaton ◽  
Bio Engineering

In this study, we first introduce several problems related to finding reset words for deterministic finite automata, and present motivations for these problems for practical applications in areas such as robotics and bio-engineering. We then analyse computational complexities of these problems. Second, we consider monotonic and partially specified automata. Monotonicity is known to be a feature simplyfing the synchronizability problems. On the other hand for partially specified automata, synchronizability problems are known to be harder than the completely specified automata. We investigate the complexity of some synchronizability problems for automata that are both monotonic and partially specified. We show that checking the existence, computing one, and computing a shortest reset word for a monotonic partially specified automaton is NP-hard. We also show that finding a reset word that synchronizes 𝓚 number of states (or maximum number of states) of a given monotonic non-synchronizable automaton to a given set of states is NP-hard.

DESCRIPTIONAL COMPLEXITY OF NFA OF DIFFERENT AMBIGUITY

2005 ◽  
Vol 16 (05) ◽  
pp. 975-984 ◽  
Author(s):  
HING LEUNG
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Finite Automata ◽  
Descriptional Complexity ◽  
Nondeterministic Finite Automata ◽  
Initial States

In this paper, we study the tradeoffs in descriptional complexity of NFA (nondeterministic finite automata) of various amounts of ambiguity. We say that two classes of NFA are separated if one class can be exponentially more succinct in descriptional sizes than the other. New results are given for separating DFA (deterministic finite automata) from UFA (unambiguous finite automata), UFA from MDFA (DFA with multiple initial states) and UFA from FNA (finitely ambiguous NFA). We present a family of regular languages that we conjecture to be a good candidate for separating FNA from LNA (linearly ambiguous NFA).

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