Operational state complexity of nested word automata

We introduce techniques to prove lower bounds for the number of states needed by finite automata operating on nested words. We study the state complexity of Boolean operations and obtain lower bounds that are tight within an additive constant. The results for union and complementation differ from corresponding bounds for ordinary finite automata. For reversal and concatenation, we establish lower bounds that are of a different order than the worst-case bounds for ordinary finite automata.     

On pebble automata for data languages with decidable emptiness problem

In this paper we study a subclass of pebble automata (PA) for data languages for which the emptiness problem is decidable. Namely, we show that the emptiness problem for weak 2-pebble automata is decidable, while the same problem for weak 3-pebble automata is undecidable. We also introduce the so-called top view weak PA. Roughly speaking, top view weak PA are weak PA where the equality test is performed only between the data values seen by the two most recently placed pebbles. The emptiness problem for this model is still decidable. It is also robust: alternating, non-deterministic and deterministic top view weak PA have the same recognition power; and are strong enough to accept all data languages expressible in Linear Temporal Logic with the future-time operators, augmented with one register freeze quantifier.     

Limitations of lower bound methods for deterministic nested word automata

Finite automata operating on nested words were introduced by Alur and Madhusudan in 2006. While nested word automata retain many of the desirable properties of ordinary finite automata, there is no known efficient minimization algorithm for deterministic nested word automata and, interestingly, state complexity bounds for nested word automata turn out to differ significantly from the corresponding bounds for ordinary finite automata. Consequently lower bounds for the state complexity of nested word languages need to rely on fooling set type techniques. We discuss limitations of the techniques and show that, even in the deterministic case, the bounds given by the lower bound methods may be arbitrarily far away from the actual state complexity of the nested word language.     

Weighted automata with discounting

We investigate weighted automata with discounting and their behaviors over semirings and finitely generated graded monoids. We characterize the discounted behaviors of weighted automata precisely as rational formal power series with a discounted form of the Cauchy product. This extends a classical result of Kleene-Schützenberger. Here we show that the very special case of Schützenberger's result for free monoids over singleton alphabets suffices to deduce our generalization.     

Approximate string matching with suffix automata

Theapproximate string matching problem is, given a text string, a pattern string, and an integerk, to find in the text all approximate occurrences of the pattern. An approximate occurrence means a substring of the text with edit distance at mostk from the pattern. We give a newO(kn) algorithm for this problem, wheren is the length of the text. The algorithm is based on the suffix automaton with failure transitions and on the diagonalwise monotonicity of the edit distance table. Some experiments showing that the algorithm has a small overhead are reported.     

Enumeration and generation with a string automata representation

The representation of combinatorial objects is decisive for the feasibility of several enumerative tasks. In this work, we present a unique string representation for complete initially-connected deterministic automata (ICDFAs) with n$n$ states over an alphabet of k$k$ symbols. For these strings we give a regular expression and show how they are adequate for exact and random generation, allow an alternative way for enumeration and lead to an upper bound for the number of ICDFAs. The exact generation algorithm can be used to partition the set of ICDFAs in order to parallelize the counting of minimal automata, and thus of regular languages. A uniform random generator for ICDFAs is presented that uses a table of pre-calculated values. Based on the same table, an optimal coding for ICDFAs is obtained.     

Stable trace automata vs. full trace automata

Trace automata provide a well-studied model for systems with concurrent behavior, which is usually given by associated domains of finite or infinite computation systems. Several authors in the literature have characterized order-theoretically these domains which are typically particular Scott domains. In most of these investigations, the question remain open when such a domain can be obtained from some finite automaton. In this paper it is shown that finite stable trace automata and finite full trace automata give rise to the same class of coherent dI-domains. The proof of this result involves combinatorial means from graph theory (colorings) and Ramsey's theorem.     

Deciding unique decodability of bigram counts via finite automata

We revisit the problem of deciding by means of a finite automaton whether a string is uniquely decodable from its bigram counts. An efficient algorithm for constructing a polynomial-size Nondeterministic Finite Automaton (NFA) that decides unique decodability is given. This NFA may be simulated efficiently in time and space. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has exponentially many states in alphabet size, and compute the correct order of magnitude of the exponent.     

Finite automata theory with membership values in lattices

In this paper, we study finite automata with membership values in a lattice, which are called lattice-valued finite automata. The extended subset construction of lattice-valued finite automata is introduced, then the equivalences between lattice-valued finite automata, lattice-valued deterministic finite automata and lattice-valued finite automata with ε-moves are proved. A simple characterization of lattice-valued languages recognized by lattice-valued finite automata is given, then it is proved that the Kleene theorem holds in the frame of lattice-setting. A minimization algorithm of lattice-valued deterministic finite automata is presented. In particular, the role of the distributive law for the truth valued domain of finite automata is analyzed: the distributive law is not necessary to many constructions of lattice-valued finite automata, but it indeed provides some convenience in simply processing lattice-valued finite automata.     

Improved constructions of mixed state quantum automata

Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A. Ambainis and R. Freivalds that quantum finite automata with pure states can have an exponentially smaller number of states than deterministic finite automata recognizing the same language. There was an unpublished “folk theorem” proving that quantum finite automata with mixed states are no more super-exponentially more concise than deterministic finite automata. It was not known whether the super-exponential advantage of quantum automata is really achievable.     

基于有限状态自动机的服务组合模型

分析了目前服务计算的研究现状和存在的问题，在D Berardi和A Wombacher的基础上提出了一种带条件的有限状态自动机模型cFSA（Finite State Automata with condition），并给出了基于cFSA的服务理论模型．在该服务理论模型的基础上提出了一种基于有限状态自动机的服务组合形式化模型，并给出了该模型的代数性质和实现方法．     

Fast string correction with Levenshtein automata

The Levenshtein distance between two words is the minimal number of insertions, deletions or substitutions that are needed to transform one word into the other. Levenshtein automata of degree n for a word W are defined as finite state automata that recognize the set of all words V where the Levenshtein distance between V and W does not exceed n. We show how to compute, for any fixed bound n and any input word W, a deterministic Levenshtein automaton of degree n for W in time linear to the length of W. Given an electronic dictionary that is implemented in the form of a trie or a finite state automaton, the Levenshtein automaton for W can be used to control search in the lexicon in such a way that exactly the lexical words V are generated where the Levenshtein distance between V and W does not exceed the given bound. This leads to a very fast method for correcting corrupted input words of unrestricted text using large electronic dictionaries. We then introduce a second method that avoids the explicit computation of Levenshtein automata and leads to even improved efficiency. Evaluation results are given that also address variants of both methods that are based on modified Levenshtein distances where further primitive edit operations (transpositions, merges and splits) are used. Received: 13 February 2002 / Accepted: 13 March 2002     

Non-structural subtype entailment in automata theory

Decidability of non-structural subtype entailment is a long-standing open problem in programming language theory. In this paper, we apply automata theoretic methods to characterize the problem equivalently by using regular expressions and word equations. This characterization induces new results on non-structural subtype entailment, constitutes a promising starting point for further investigations on decidability, and explains for the first time why the problem is so difficult. The difficulty is caused by implicit word equations that we make explicit.     

Matrix expression and reachability analysis of finite automata

In this paper,we propose a matrix-based approach for finite automata and then study the reachability conditions.Both the deterministic and nordeterministic automata are expressed in matrix forms,and th...     

Sufficient conditions of deterministic implementation of finite-state automata with retention of the numbers of their states

The following three conditions for nondeterministic finite-state automata are defined: input embeddability, output embeddability, and input decomposability. Automata satisfying these conditions are called nondeterministic automata with embeddability. A method for deterministic implementation of such automata with retention of the numbers of their states is proposed. These automata correspond to block-procedural high-level programming languages. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 55–62, May–June, 2000.     

模糊识别器与有穷自动机的等价性

针对模糊识别器与有穷自动机的关系,证明了当输入字母表相同时,任给一个模糊识别器,必然存在一个有穷自动机,使得模糊识别器的行为与有穷自动机所接受的语言相同;反之,任给一个有穷自动机,必然存在一个模糊识别器,使得有穷自动机所接受的语言与模糊识别器的行为相同,从而得出它们之间的等价性。     

Scheduling with timed automata

In this work, we present timed automata as a natural tool for posing and solving scheduling problems. We show how efficient shortest path algorithms for timed automata can find optimal schedules for the classical job-shop problem. We then extend these results to synthesize adaptive scheduling strategies for problems with uncertainty in task durations.