Showing papers on "ω-automaton published in 1993"

Asynchronous Mappings and Asynchronous Cellular Automata

Abstract: The aim of this paper is the study of asynchronous automata, a special kind of automata which encode the independency relation between actions and which enable their concurrent execution. These automata, introduced by Zielonka (RAIRO Inform. Theor. Appl.21, 99-135 (1987)), constitute a natural extension of finite automata to the case of asynchronous parallelism. Their behaviour is described by trace languages, subsets of partially commutative monoids. The main result concerning this class of automata states that they accept exactly all recognizable trace languages. In this paper we give new improved constructions of asynchronous automata. In the final part of the paper we present a distributed system of messages with bounded time-stamps based on asynchronous automata.

A taxonomy of finite automata minimization algorithms

Abstract: This paper presents a taxonomy of finite automata minimization algorithms. Brzozowski's elegant minimization algorithm differs from all other known minimization algorithms, and is derived separately. All of the remaining algorithms depend upon computing an equivalence relation on states. We define the equivalence relation, the partition that it induces, and its complement. Additionally, some useful properties are derived. It is shown that the equivalence relation is the greatest fixed point of an equation, providing a useful characterization of the required computation. We derive an upperbound on the number of approximation steps required to compute the fixed point. Algorithms computing the equivalence relation (or the partition, or its complement) are derived systematically in the same framework. The algorithms include Hopcroft's, several algorithms from text-books (including Hopcroft and Ullman's [HU79], Wood's [Wood87], and Aha, Sethi, and Ullman's [ASU86]), and several new algorithms or variants of existing algorithms.

Efficient learning of typical finite automata from random walks

Abstract: This paper describes new and efficient algorithms for learning deterministic finite automata. Our approach is primarily distinguished by two features: (1) the adoption of an average-case setting to model the ``typical'' labeling of a finite automaton, while retaining a worst-case model for the underlying graph of the automaton, along with (2) a learning model in which the learner is not provided with the means to experiment with the machine, but rather must learn solely by observing the automaton's output behavior on a random input sequence. The main contribution of this paper is in presenting the first efficient algorithms for learning nontrivial classes of automata in an entirely passive learning model. We adopt an on-line learning model in which the learner is asked to predict the output of the next state, given the next symbol of the random input sequence; the goal of the learner is to make as few prediction mistakes as possible. Assuming the learner has a means of resetting the target machine to a fixed start state, we first present an efficient algorithm that article no. IC972648

Encompassment Properties and Automata with Constraints

Abstract: We introduce a class of tree automata with constraints which gives an algebraic and algorithmic framework in order to extend the theorem of decidability of inductive reducibility. We use automata with equality constraints in order to solve encompassment constraints and we combine such automata in order to solve every first order formulas built up with unary predicates “x encompasses t” denoted by encompt(x).

Solving Systems of Set Constraints using Tree Automata

Abstract: A set constraint is of the form exp1\(\subseteq\)exp2 where exp1 and exp2 are set expressions constructed using variables, function symbols, and the set union, intersection and complement symbols. An algorithm for solving such systems of set constraints was proposed by Aiken and Wimmers [1]. We present a new algorithm for solving this problem. Indeed, we define a new class of tree automata called Tree Set Automata. We prove that, given a system of set constraints, we can associate a tree set automaton such that the set of tuples of tree languages recognized by this automaton is the set of tuples of solutions of the system. We also prove the converse property. Furthermore, if the system has a solution, we prove, in a constructive way, that there is a regular solution (i.e. a tuple of regular tree languages) and a minimal solution and a maximal solution which are actually regular.

A taxonomy of finite automata construction algorithms

Abstract: This paper presents a taxonomy of finite automata construction algorithms. Each algorithm is classified into ODe of two families: those based upon the structure of regular expressions, and those based upon the automata-theoretic work of Myhill and Nerode. Many of the algorithms appearing in the literature are based upon the structure of regular expressions. In this paper, we make this term precise by defining regular expressions as a ~>term algebra, and automata constructions as various E-algebras of automata. Each construction algorithm is then presented as the unique natural homomorphism from the Eterm algebra of regular expressions to the appropriate E-algebra of automata. The concept of duality is introduced and used to derive more practical construction algorithms. In this way, we successfully present (and relate) algorithms given by Thompson, Berry and Sethi, McNaughton and Yamada, Glushkov, and Aho, Sethi, and Ullman. Efficient implementations (including those due to Chang and Paige, and Briiggemann-Klein) are also treated. As a side-effect we derive several new algorithms. A pair of impractical, but theoretically interesting, construction algorithms were presented by Myhill and Nerode. Some encoding techniques are used to make the algorithms practical giving Brzozowski's algorithm based upon derivatives. DeRemer's algorithm is derived as an encoding of Brzozowski's algorithm. Two new algorithms, related to DeRemer's, are derived. Lastly, this family of algorithms is related to the first family. In addition to classifying the algorithms, we identify (and abstract from) the coding tricks and implementation details present in many of the published algorithms. This paper also presents an introduction to finite automata, E-algebras, and their properties.

Domains of Higher-Dimensional Automata

Abstract: We carry on the program set up in [GJ92] by giving constructions of “domains of higher-dimensional automata (HDA)” on which we can define the truly-concurrent semantics of parallel languages, much in the style of domain theory (see [GS90]). In [GJ92] we gave a semantics for CCS-like languages. In this article, we show how to extend the technique to languages with real states, while keeping nice algebraic definitions. In particular, we are still able to compute local invariants which can decide a few computational properties of interest. For being used as actual computational definitions, the semantics is denotational (i.e. compositional); for being precise enough when it comes to studying the dynamic behaviour of programs, the denotations are higher-dimensional automata, which are no more than an operational behaviour (in the style of operational semantics, see [Plo81]). We conclude by giving the semantics of a small shared-memory imperative language.

Distributed control methods

Abstract: The distributed system is becoming increasingly popular, and this produces the need for more sophisticated distributed control techniques. The authors present a method for distributed control using simple finite state automata. Each of the distributed entities is 'controlled' by its associated automaton, in the sense that the entity examines the state of the automaton to determine its behavior. The result of the collective behavior of all of the entities is fed back to the automata, which change their state as a result of this feedback. They give a new method of analysis which derives the steady state behavior of this system as a whole, by decomposing it into two parts: describing and solving an imbedding auxiliary Markov chain, and analyzing the behavior of the system within each of the states of this auxiliary chain. >

Branching Time Temporal Logic and Amorphous Tree Automata

Abstract: An automata-theoretic framework for branching-time temporal logics is presented. We introduce a new type of finite automata on infinite trees, the amorphous automata, and use them as a formalism to represent efficiently CTL formulas. In addition, we introduce simultaneous trees, and associate with every model for CTL, a simultaneous tree that enables a tree automaton to visit different nodes on the same path of the tree simultaneously. With every formula ψ, we associate an amorphous automaton Uψ, that accepts exactly those simultaneous trees (of any branching degree) that originate from models that satisfy ψ. This enables to use the automaton both for model checking which is reduced to the membership problem, and for satisfiability decision, which is reduced to testing the nonemptiness of an extension of Uψ that does not assume simultaneous input trees.

Rewriting and Tree Automata

Abstract: We summarize the main connections between rewriting, automata, and logical languages. We recall and illustrate from a rewriting point of view classical tree automata, Rabin and Buchi automata, which are associated with (W)SIS and (W)SkS logics. We introduce four recent classes of tree automata, closely linked to rewriting problems.

Distance automata having large finite distance or finite ambiguity

Abstract: A distance automaton is a (nondeterministic finite) automaton which is equipped with a nonnegative cost function on its transitions. The distance of a word recognized by such a machine quantifies the expenses associated with the recognition of this word. The distance of a distance automaton is the maximal distance of a word recognized by this machine or is infinite, depending on whether or not a maximum exists. We present distance automata havingn states and distance 2 n − 2. As a by-product we obtain regular languages having exponential finite order. Given a finitely ambiguous distance automaton withn states, we show that either its distance is at most 3 n − 1, or the growth of the distance in this machine is linear in the input length. The infinite distance problem for these distance automata is NP-hard and solvable in polynomial space. The infinite-order problem for regular languages is PSPACE-complete.

Self-Modifying Finite Automata.

Abstract: We present here a new model of computation: the Self-Modifying Finite Automaton (SMFA). This is similar to a standard nite automaton, but changes to the machine are allowed during a computation. It is shown here that a weak form of this model has the power to recognize an important class of context-free languages, the metalinear languages, as well as some signi cant non-context-free languages. Less restricted forms of SMFA's may accept even more.

New Decidability Results Concerning Two-way Counter Machines and Applications

Abstract: We look at some decision questions concerning two-way counter machines and obtain the strongest decidable results to date concerning these machines. In particular, we show that the emptiness, containment, and equivalence problems are decidable for two-way counter machines whose counter is reversal-bounded (i.e., the counter alternates between increasing and decreasing modes at most a fixed number of times). We use this result to give a simpler proof of a recent result that the emptiness, containment, and equivalence problems for two-way reversal-bounded pushdown automata accepting bounded languages (i.e., subsets of w 1 * ... w k * for some nonnull words w1,...,wk) are decidable. Other applications concern decision questions about simple programs. Finally, we show that nondeterministic two-way reversal-bounded multicounter machines are effectively equivalent to finite automata on unary languages, and hence their emptiness, containment, and equivalence problems are decidable also.

Concise representations of regular languages by degree and probabilistic finite automata

Abstract: Meyer and Fischer b][MF] proved that nondeterministic finite automata (NFA) can be exponentially more concise than deterministic finite automata (DFA) in their representations of regular languages. Several variants of that basic finite state machine model are now being used to analyze parallelism and to build real-time software systems [HL+]. Even though these variants can sometimes represent regular languages in a more concise manner than NFA, the underlying models fundamentally differ from NFA in how they operate. Degree automata [W] (DA), however, differ from NFA only in their acceptance criteria and accept only regular languages. We show here that DA are also exponentially more concise than NFA on some sequences of regular languages. We also show that the conciseness of probabilistic automata [R] with isolated cutpoints can be unbounded over DA and, concurrently, i.e., over the same sequence of languages, those DA can be exponentially more concise than NFA.

The VC-Dimensions of Finite Automata with n States

Abstract: In this paper, we investigate the VC-dimensions of finite automata. We show that for a fixed positive integer k (1) the VC-dimension of DFAk,n, which is the class of dfas of an alphabet size k whose minimum states dfa has at most n states, is (k− 1+o(1))n log n, (2) the VC-dimension of NFAk,n, which is the class of nfas of an alphabet size k whose minimum states nfa has at most n states, is Q(n2) and (3) the VC-dimension of CDFAk,n, which is the class of commutative dfas of an alphabet size k whose minimum states commutative dfas has at most n states, is (1+o(1))n. These results are applied to the problems in computational learning theory.

On the correctness of some algorithms to generate finite automata for regular expressions

Abstract: We discuss the method given by Glushkov, McNaughton-Yamada and Berry-Sethi and a related method given by Aho, Sethi and Ullmann to generate a deterministic finite automaton accepting the language of a given regular expression For both methods a formal description and a simple correctness proof is given

Learning fallible finite state automata

Abstract: We consider the problem of learning from a fallible expert that answers all queries about a concept, but often gives incorrect answers. The expert can also be thought of as a truth table describing the concept which has been partially corrupted. In order to learn the underlying concept with arbitrarily high precision, we would like to use its structure in order to correct most of the incorrect answers. We assume that the expert’s errors are uniformly and independently distributed, occur with any probability strictly smaller than ~, and are persistent. In particular, we present a polynomial time algorithm using membership queries for correcting and learning fallible DFA’s under the uniform distribution.

A cooperative path-planning for multiple automata by dynamic/static conversion

Abstract: An online path-planning algorithm for multiple automata is proposed. Each automaton usually goes straight to the goal. When some of the automata touch each other, some kind of swarm occurs and is identified by sensors. In general, several kinds of swarm appear, since a lot of automata collide in different circumstances. The proposed algorithm decomposes all simple and complex swarms uniformly by the following dynamic/static conversion: some automata are stopped in the swarm, and the others are moved around the set of stopped automata. By using this conversion, the algorithm destroys all swarms by some simple motions in common and is easily applied for some practical robots. Moreover, the automata decompose the swarm by cooperative motions as follows: an inside automaton comes close to its goal monotonously. Since all automata go straight to their goals outside the swarm, convergence of the automata toward their goals is naturally ensured. Communication overhead is kept small enough by using the monotony property, and consequently the algorithm can run online.

Universal Computation in Few-body Automata.

Abstract: Few-body automata are a class of cellular automata. They were developed specifically to investigate the possibility of implementing a new generation of cellular automata machines that would use dense arrays of nanometer-scale device-cells. In this paper, we try to determine how many states per cell are required by few-body automata in order to perform universal computation. We prove theorems describing the space, time, and state-set complexity of the simulation of d-dimensional conventional cellular automata with N-body automata, and show that there exist computation-universal 2-body automata requiring 5.81 bits of state per cell for d = 1 and 2 bits per cell for d = 2. These results suggest that physically-imposed restrictions on the number of available bits per cell will not be an obstacle to cellular automaton-like computation at nanometer scales.

Separating Exponentially Ambiguous NFA from Polynomially Ambiguous NFA

Abstract: We resolve an open problem raised by Ravikumar and Ibarra on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {An} over a two-letters alphabet such that, for any positive integer n, An is exponentially ambiguous and has n states, whereas the smallest equivalent deterministic finite automaton has 2n states and any smallest equivalent polynomially ambiguous finite automaton has 2n− 1 states.

Local Automata and Completion

Abstract: The problem of completing a finite automata preserving its properties is here investigated in the case of deterministic local automata. We show a decision procedure and give an algorithm which complete a deterministic local automaton (if the completion exists) with another one, having the same number of states.

Learning Finite Automata Using Local Distinguishing Experiments.

Abstract: One of the open problems listed in Rivest and Schapire is whether and how that the copies of L in their algorithm can be com bined into one for better performance This paper describes an algorithm called D that does that combination The idea is to represent the states of the learned model using observable symbols as well as hidden symbols that are con structed during learning These hidden sym bols are created to re ect the distinct behaviors of the model states The distinct behaviors are represented as local distinguishing experiments LDEs not to be confused with global distin guishing sequences and these LDEs are cre ated when the learner s prediction mismatches the actual observation from the unknown ma chine To synchronize the model with the en vironment these LDEs can also be concate nated to form a homing sequence It can be shown that D can learn with probability a model that is an approximation of the unknown machine in a number of actions polynomial in the size of the environment and log

Forming grammars for structured documents

Abstract: We consider the problem of finding a small regular grammar that correctly describes the structure of a large text with named components. Examples of such texts are dictionaries, user manuals, business letters, and so on. A structural description in the form of the regular grammar can be used, e.g., to help in retrieving information from the document. We start by constructing for each named component of the document a weighted finite-state automaton that accepts all the structures for that component that are present in the original document. The weight of a transition shows how many times the transition is used in the original document. This automaton is generalized by merging states and updating the weights until the automaton satisfies a certain context condition. The automata corresponding to different components in the document are also generalized with respect to each other. The generalized weighted automata are transformed into a series of regular expressions corresponding to the heavy paths in the automata.

One dimensional dynamics and factors of finite automata

Abstract: We argue that simple dynamical systems are factors of finite automata, regarded as dynamical systems on discontinuum. We show that any homeomorphism of the real interval is of this class. An orientation preserving homeomorphism of the circle is a factor of a finite automaton iff its rotation number is rational. Any $S$-unimodal system on the real interval, whose kneading sequence is either periodic odd or preperiodic, is also a factor of a finite automaton, while $S$-unimodal systems at limits of period doubling bifurcations are not.

The effect of the number of successful paths in a büchi tree automaton

Abstract: We modify an acceptance condition of Buchi automaton on infinite trees: rather than to require that each computation path is successful, we impose various restrictions on the number of successful paths in a run of the automaton on a tree. All these modifications alter the recognizing power of Buchi automata. We examine the classes induced by the acceptance conditions that require ≤α, ≥α, =α successful paths, where α is a cardinal number. It turns out that, except for some trivial cases, the “≤” classes are incomparable with the class Bu of Buchi acceptable tree languages, while the classes “≥” are strictly included in Bu.