Showing papers on "ω-automaton published in 1996"

Does a Rock Implement Every Finite-State Automaton?

Abstract: Hilary Putnam has argued that computational functionalism cannot serve as a foundation for the study of the mind, as every ordinary open physical system implements every finite-state automaton. I argue that Putnam's argument fails, but that it points out the need for a better understanding of the bridge between the theory of computation and the theory of physical systems: the relation of implementation. It also raises questions about the class of automata that can serve as a basis for understanding the mind. I develop an account of implementation, linked to an appropriate class of automata, such that the requirement that a system implement a given automaton places a very strong constraint on the system. This clears the way for computation to play a central role in the analysis of mind.

Representation of finite state automata in recurrent radial basis function networks

Abstract: In this paper, we propose some techniques for injecting finite state automata into Recurrent Radial Basis Function networks (R2BF). When providing proper hints and constraining the weight space properly, we show that these networks behave as automata. A technique is suggested for forcing the learning process to develop automata representations that is based on adding a proper penalty function to the ordinary cost. Successful experimental results are shown for inductive inference of regular grammars.

On the Degree of Ambiguity of Finite Automata

Abstract: We show that the degree of ambiguity of a nondeterministic finite automaton (NFA) with n states, if finite, is not greater than 2n·log2n + c1·n (c1 ≅ 2.0566). We present an algorithm which decides in polynomial time whether the degree of ambiguity of a NFA is finite or not. Additionally, the authors obtain in [14] a corresponding upper bound for the finite valuedness of a normalized finite transducer (NFT), and also a polynomial-time algorithm which decides whether the valuedness of a NFT is finite or not.

Finite time analysis of the pursuit algorithm for learning automata

Abstract: The problem of analyzing the finite time behavior of learning automata is considered. This problem involves the finite time analysis of the learning algorithm used by the learning automaton and is important in determining the rate of convergence of the automaton. In this paper, a general framework for analyzing the finite time behavior of the automaton learning algorithms is proposed. Using this framework, the finite time analysis of the Pursuit Algorithm is presented. We have considered both continuous and discretized forms of the pursuit algorithm. Based on the results of the analysis, we compare the rates of convergence of these two versions of the pursuit algorithm. At the end of the paper, we also compare our framework with that of Probably Approximately Correct (PAC) learning.

On the Power of Non-Observable Actions in Timed Automata

Abstract: Timed finite automata, introduced by Alur and Dill, are one of the most widely studied models for real-time systems. We focus in this paper on the power of silent transitions, i.e. e-transitions, in such automata. We show that e-transitions strictly increase the power of timed automata and that the class of timed languages recognized by automata with e-transitions is much more robust than the corresponding class without e-transitions. Our main result shows that these transitions increase the power of these automata only if they reset clocks.

The Complexity of Probabilistic versus Deterministic Finite Automata

Abstract: We show that there exists probabilistic finite automata with an isolated cutpoint and n states such that the smallest equivalent deterministic finite automaton contains \(\Omega \left( {2^{n\tfrac{{\log \log n}}{{\log n}}} } \right)\) states.

The Theory of Rectangular Hybrid Automata

Abstract: A {\em hybrid automaton\/} consists of a finite automaton interacting with a dynamical system. Hybrid automata are used to model embedded controllers and other systems that consist of interacting discrete and continuous components. A hybrid automaton is {\em rectangular\/} if each of its continuous variables~$x$ satisfies a nondeterministic differential equation of the form $a\le\frac{dx}{dt}\le b$, where $a$ and~$b$ are rational constants. Rectangular hybrid automata are particularly useful for the analysis of communication protocols in which local clocks have bounded drift, and for the conservative approximation of systems with more complex continuous behavior. We examine several verification problems on the class of rectangular hybrid automata, including reachability, temporal logic model checking, and controller synthesis. Both dense-time and discrete-time models are considered. We identify subclasses of rectangular hybrid automata for which these problems are decidable and give complexity analyses. An investigation of the structural properties of rectangular hybrid automata is undertaken. One method for proving the decidability of verification problems on infinite-state systems is to find finite quotient systems on which analysis can proceed. Three state-space equivalence relations with strong connections to temporal logic are bisimilarity, similarity, and language equivalence. We characterize the quotient spaces of rectangular hybrid automata with respect to these equivalence relations.

Two-way automata and length-preserving homomorphisms

Abstract: Closure underlength-preserving homomorphisms is interesting because of its similarity tonondeterminism. We give a characterization of NP in terms of length-preserving homomorphisms and present related complexity results. However, we mostly study the case of two-way finite automata: Let l.p.hom[n state 2DFA] denote the class of languages that are length-preserving homomorphic images of languages recognized byn-state 2DFAs. We give a machine characterization of this class. We show that any language accepted by ann-state two-wayalternating finite automaton (2AFA), or by a l-pebble 2NFA, belongs to l.p.hom[O(n 2) state 2DFA]. Moreover, there are languages in l.p.hom[n state 2DFA] whose smallest accepting 2NFA has at leastc n states (for some constantc > 1). So for two-way finite automata, the closure under length-preserving homomorphisms is much more powerful than nondeterminism. We disprove two conjectures (of Meyer and Fischer, and of Chrobak) about the state-complexity of unary languages. Finally, we show that the equivalence problems for 2AFAs (resp. 1-pebble 2NFAs) are in PSPACE, and that the equivalence problem for 1-pebble 2AFAs is in ExpSPACE (thus answering a question of Jiang and Ravikumar); it was known that these problems are hard in these two classes. We also give a new proof that alternating 1-pebble machines recognize only regular languages (which was first proved by Goralciket al.).

Multimodal searching technique based on learning automata with continuous input and changing number of actions

Abstract: This paper describes a multimodal searching technique based on a stochastic automaton. The environment where the automaton operates corresponds to the function to be optimized which is assumed to be unknown function of a single parameter x. The admissible region of x is quantized into N subsets. The environment response is continuous (S-model). The complete set of actions of the automaton is divided into nonempty subsets. The action set is changing from instant to instant and is selected based on a probability distribution. These actions are in turn associated with the discrete values of the parameter x. Convergence and convergence rate results are presented. Simulation results illustrate the performance of this searching technique.

Unitarity in one dimensional nonlinear quantum cellular automata

Abstract: Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which precludes nontrivial homogeneous evolution for linear quantum cellular automata. Here we carefully define general quantum cellular automata in order to investigate the possibility that there be nontrivial homogeneous unitary evolution when the local rule is nonlinear. Since the unitary global transition amplitudes are constructed from the product of local transition amplitudes, infinite lattices require different treatment than periodic ones. We prove Unitarity Theorems for both cases, expressing the equivalence in 1+1 dimensions of global unitarity and certain sets of constraints on the local rule, and then show that these constraints can be solved to give a variety of multiparameter families of nonlinear quantum cellular automata. The Unitarity Theorems, together with a Surjectivity Theorem for the infinite case, also imply that unitarity is decidable for one dimensional cellular automata.

Relating word and tree automata

Abstract: In the automata-theoretic approach to verification, we translate specifications to automata. Complexity considerations motivate the distinction between different types of automata. Already in the 60's, it was known that deterministic Buchi word automata are less expressive than nondeterministic Buchi word automata. The proof is easy and can be stated in a few lines. In the late 60's, Rabin proved that Buchi tree automata are less expressive than Rabin tree automata. This proof is much harder. In this work we relate the expressiveness gap between deterministic and nondeterministic Buchi word automata and the expressiveness gap between Buchi and Rabin tree automata. We consider tree automata that recognize derived languages. For a word language L, the derived language of L, denoted L/spl Delta/, is the set of all trees all of whose paths are in L. Since often we want to specify that all the computations of the program satisfy some property, the interest in derived languages is clear. Our main result shows that L is recognizable by a nondeterministic Buchi word automaton but not by a deterministic Buchi word automaton iff L/spl Delta/ is recognizable by a Rabin tree automaton and not by a Buchi tree automaton. Our result provides a simple explanation to the expressiveness gap between Buchi and Rabin tree automata. Since the gap between deterministic and nondeterministic Buchi word automata is well understood, our result also provides a characterization of derived languages that can be recognized by Buchi tree automata. Finally, it also provides an exponential determinization of Buchi tree automata that recognize derived languages.

Multiple response learning automata

Abstract: Learning Automata update their action probabilites on the basis of the response they get from a random environment. They use a reward adaptation rate for a favorable environment's response and a penalty adaptation rate for an unfavorable environment's response. In this correspondence, we introduce Multiple Response learning automata by explicitly classifying the environment responses into a reward (favorable) set and a penalty (unfavorable) set. We derive a new reinforcement scheme which uses different reward or penalty rates for the corresponding reward (favorable) or penalty (unfavorable) responses. Well known learning automata, such as the L/sub R-P/;L/sub R-I/; L/sub R-eP/ are special cases of these Multiple Response learning automata. These automata are feasible at each step, nonabsorbing (when the penalty functions are positive), and strictly distance diminishing. Finally, we provide conditions in order that they are ergodic and expedient.

Forgetting automata and context-free languages

Abstract: It is shown that context-free languages can be characterized by linear bounded automata with the following restriction: the head can either move right without rewriting or move left with erasing the current cell (i.e. rewriting it with a special, nonrewriteable, symbol). If, instead of erasing, we consider deleting (complete removing of the cell), the corresponding automata are less powerful.

Matrices, machines and behaviors

Abstract: Sabadini, Walters and others have developed a categorical, machine based theory of concurrency in which there are four essential aspects: a distributive category of data-types; a bicategory Mach whose objects are data types, and whose arrows are input-output machines built from data types; a semantic category (or categories) Sem, suitable to contain the behaviors of machines, and a functor, “behavior”: Mach→Sem. Suitable operations on machines and semantics are found so that the behavior functor preserves these operations. Then, if each machine is decomposable into primitive machines using these operations, the behavior of a general machine is deducible from the behavior of its parts. The theory of non-deterministic finite state automata provides an example of the paradigm and also throws some light on the classical theory of finite state automata. We describe a bicategory whose objects are natural numbers, in which an arrow M: n→p is a finite state automaton with n input states, p output states, and some additional internal states; we require that no transitions begin at output states or end at input states. A machine is represented by an q+n by q+p matrix. The bicategory supports additional operations: non-deterministic choice, parallel interleaving, and feedback. Enough operations are imposed on machines to show that each machine may be obtained from some atomic ones by means of the operations. The semantic category is the (Bloom-Esik) iteration theory Mat (X✶ whose objects are natural numbers and whose arrows from n to p are n×p matrices with entries in the semiring of languages. The behavior functor associates to a machine M: n→p a matrix |M| of languages, one language to each pair of input and output states. Behavior preserves composition, feedback, takes non-deterministic choice to union, and parallel-interleaving to shuffle. Thus, behavior gives a compositional semantics to a primitive notion of concurrent processes.

Learning two-tape automata from queries and counterexamples

Abstract: We investigate the learning problem of two-tape deterministic finite automata (2-tape DFAs) from queries and counterexamples. Instead of accepting a subset of ∑*, a 2-tape DFA over an alphabet ∑ accepts a subset of ∑* × ∑*, and therefore, it can specify a binary relation on ∑*. In [3] Angluin showed that the class of deterministic finite automata (DFAs) is learnable in polynomial time from membership queries and equivalence queries, namely, from a minimally adequate teacher (MAT). In this article we show that the class of 2-tape DFAs is learnable in polynomial time from MAT. More specifically, we show an algorithm that, given any languageL accepted by an unknown 2-tape DFAM, learns from MAT a two-tape nonde-terministic finite automaton (2-tape NFA)M′ acceptingL in time polynomial inn andl, wheren is the size ofM andl is the maximum length of any counterexample provided during the learning process.

Numerical Issues for Stochastic Automata Networks

Abstract: In this paper we consider some numerical issues in computing solutions to networks of stochastic automata (SAN). In particular our concern is with keeping the amount of computation per iteration to a minimum, since iterative methods appear to be the most effective in determining numerical solutions. In a previous paper we presented complexity results concerning the vector-descriptor multiplication phase of the analysis. In this paper our concern is with implementation details. We experiment with the size and sparsity of individual automata; with the ordering of the automata; with the percentage and location of functional elements; with the occurrence of different types of synchronizing events and with the occurrence of cyclic dependencies within terms of the descriptor. We also consider the possible benefits of grouping many small automata in a SAN with many small automata to create an equivalent SAN having a smaller number of larger automata.

Computing the Rabin Index of a Regular Language of Infinite Words

Abstract: The Rabin index of a regular language of infinite words is the minimum number of accepting pairs used in any deterministic Rabin automaton recognizing this language. We show that the Rabin index of a language given by a Muller automaton withnstates andmaccepting sets is computable in timeO(m2nc) wherecis the cardinality of the alphabet.

Probabilistic asynchronous automata

Abstract: Asynchronous automata were introduced by W. Zielonka as an algebraic model of distributed systems, showing that the class of trace languages recognizable by automata over free partially commutative monoids coincides with the class of trace languages recognizable by deterministic asynchronous automata. In this paper we extend the notion of asynchronous automata to the probabilistic case. Our main result is a nontrivial generalization to Zielonka's theorem: we prove that the sets of behaviors of probabilistic automata and of probabilistic asynchronous automata coincide in the case of concurrent alphabets with acyclic dependency graphs.

Elements of an automata theory over partial orders.

Abstract: A model of nondeterministic nite automaton over ((nite) partial orders is introduced. It captures existential monadic second-order logic in expressive power and generalizes classical word automata and tree automata. Special forms, such as deterministic automata, are discussed, and logical and algorithmic properties are analyzed, like closure under complement and decid-ability of the nonemptiness problem. These questions are studied in the context of diierent classes of partial orders, such as trees, Mazurkiewicz traces, or rectangular grids.

On computational power of weighted finite automata

Abstract: Weighted Finite Automata are automata with multiplicities used to compute real functions by reading infinite words. The aim of this paper is to study what kind of functions can be computed by level automata, a particular subclass of WFA. Several results concerning the continuity and the smoothness of these functions are shown. In particular, the only smooth functions that can be obtained are the polynomials. This enables to decide whether a function computed by a level automaton is smooth or not.

On the complementation of asynchronous cellular Bu¨chi automata

Abstract: We present direct subset automata constructions for asynchronous (asynchronous cellular, resp.) automata. This provides a solution to the problem of direct determinization for automata with distributed control for languages of finite traces. We use the subset automaton construction and apply Klarlund's progress measure technique in order to complement non-deterministic asynchronous cellular Buchi automata for infinite traces. Both constructions yield a super-exponential blow-up in the size of local states sets.

Confluent Preorder Parser as Finite State Automata

Abstract: We present the Confluent Preorder Parser (CPP) in which syntactic parsing is achieved via a holistic transformation from the sentence representation to the desired parse tree representation. Simulation results show that CPP has achieved excellent generalization performance and is capable of handling erroneous sentences and resolving syntactic ambiguities. An analysis is presented which elucidates the operations of CPP as governed by a finite state automaton. The parsing is interpreted as a series of decision makings during the process. Based on this formalism, syntactic parsing and generalization by CPP can be explained in terms of state transitions.