Showing papers on "ω-automaton published in 1995"

What's decidable about hybrid automata?

Abstract: Hybrid automata model systems with both digital and analog components, such as embedded control programs. Many verification tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify the precise boundary between decidability and undecidability of the reachability problem for hybrid automata. On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow trajectories within piecewise-linear envelopes and are reinitialized whenever the envelope changes. Our algorithm is based on the construction of a timed automaton that contains all reachability information about a given initialized rectangular automaton. The translation has practical significance for verification, because it guarantees the termination of symbolic procedures for the reachability analysis of initialized rectangular automata. The translation also preserves the $\omega$-languages of initialized rectangular automata with bounded nondeterminism. On the negative side, we show that several slight generalizations of initialized rectangular automata lead to an undecidable reachability problem. In particular, we prove that the reachability problem is undecidable for timed automata augmented with a single stopwatch.

Hybrid Automata with Finite Bisimulatioins

Abstract: The analysis, verification, and control of hybrid automata with finite bisimulations can be reduced to finite-state problems. We advocate a time-abstract, phase-based methodology for checking if a given hybrid automaton has a finite bisimulation. First, we factor the automaton into two components, a boolean automaton with a discrete dynamics on the finite state space \(\mathbb{B}\) m and a euclidean automaton with a continuous dynamics on the infinite state space ℝ n . Second, we investigate the phase portrait of the euclidean component. In this fashion, we obtain new decidability results for hybrid systems as well as new, uniform proofs of known decidability results.

From Timed Automata to Logic - and Back

Abstract: One of the most successful techniques for automatic verification is that of model checking. For finite automata there exist since long extremely efficient model-checking algorithms, and in the last few years these algorithms have been made applicable to the verification of real-time automata using the region-techniques of Alur and Dill. In this paper, we continue this transfer of existing techniques from the setting of finite (untimed) automata to that of timed automata. In particular, a timed logic L is put forward, which is sufficiently expressive that we for any timed automaton may construct a single characteristic L formula uniquely characterizing the automaton up to timed bisimilarity. Also, we prove decidability of the satisfiability problem for L with respect to given bounds on the number of clocks and constants of the timed automata to be constructed. None of these results have as yet been succesfully accounted for in the presence of time.

From Timed Automata to Logic - and Back

Abstract: In this paper, we define a timed logic L v which is sufficiently expressive that we for any timed automaton may construct a single characteristic L v formula uniquely characterizing the automaton up to timed bisimilarity.

On the sofic limit sets of cellular automata

Abstract: It is not known in general whether any mixing sofic system is the limit set of some one-dimensional cellular automaton. We address two aspects of this question. We prove first that any mixing almost of finite type (AFT) sofic system with a receptive fixed point is the limit set of a cellular automaton, under which it is attained in finite time. The AFT condition is not necessary: we also give examples of non-AFT sofic systems having the same properties. Finally, we show that near Markov sofic systems (a subclass of AFT sofic systems) cannot be obtained as limit sets of cellular automata at infinity.

On Emptiness and Counting for Alternating Finite Automata.

Abstract: This invention relates to an improvement in a transverse, force-connected body with variable profiling, particularly an airplane wing, containing flexible upper, lower, and nose skin parts and supporting elements hingedly engaging thereat in conjunction with a control gear, the improvement comprising clamps securing the upper and lower flexible skin parts at a rigid part of the wing, rigid carriers in the upper and lower areas of the wing, and shaped profile elements on the upper and lower carriers, the shaped profile elements having outwardly-pointing shaped profile surfaces for the selective support of the flexible skin parts.

On control of systems modelled as deterministic Rabin automata

Abstract: Recent results on the control of infinite behaviour of finite automata are extended to allow Rabin acceptance conditions as modelling assumptions as well as specifications. The key result is a fixpoint characterization of the automaton'scontrollability subset—the set of states from which it can be controlled to the satisfaction of its associated specification. The fixpoint characterization allows for straightforward computation of the subset and for effective synthesis of controllers. the results have potential applications to supervisory control synthesis, the synthesis of reactive systems, and decision procedures for modal logics.

Finite Acceptance of Infinite Words.

Abstract: In this paper we consider the following two types of finite acceptance of infinite words by finite automata: An infinite word ξ is accepted if and only if there is a run on input ξ for which 1. (1) an accepting state is visited at least once, or 2. (2) an accepting state is visited at least once but only finitely often. The resulting classes of regular ω-languages are characterized by language-theoretic means, and they are positioned into the known hierarchies of regular ω-languages.

Partial derivatives of regular expressions and finite automata constructions

Abstract: We introduce a notion of a partial derivative of a regular expression. It is a generalization to the non-deterministic case of the known notion of a derivative invented by Brzozowski. We give a constructive definition of partial derivatives, study their properties, and employ them to develop a new algorithm for turning regular expressions into relatively small NFA and to provide certain improvements to Brzozowski's algorithm constructing DFA. We report on a prototype implementation of our algorithm constructing NFA and present some examples.

Some Results Concerning Two-Dimensional Turing Machines and Finite Automata

Abstract: We show that emptiness is decidable for three-way two-dimensional nondeterministic finite automata as well as the universe problem for the corresponding class of deterministic automata. Emptiness is undecidable for three-way (and even two-way) two-dimensional alternating finite automata over a single-letter alphabet. Consequently inclusion, equivalence, and disjointness for these automata are undecidable properties.

Discrete-Event System Theory: An Introduction

Abstract: Automata's theory - a basic elementary approach automata's theory - an algebraic approach non-deterministic automata's theory Markov's chains elementary queueing theory queueing networks.

Automata with sensing heads

Abstract: Automata that can detect coincidence of heads (sensing heads) are investigated. It is shown that several types of storage can be used for simulating sensing heads with ordinary heads. Then a general technique for separating automata with an increasing number of sensing heads on unary input alphabets is presented. Finite automata with sensing heads, pebble automata, and bounded counter automata are compared. On unary input pebble automata and finite sensing head automata are equivalent which implies a hierarchy of languages accepted by automata with an increasing number of pebbles. Finally decision problems for one-way finite sensing head automata on unary input alphabets are classified. >

Finite automata and morphisms in assisted musical composition

Abstract: Finite automata originated in computer science and linguistics. They have applications in mathematics and physics and they have already been used in assisted musical composition. In this article we show how finite automata (or more generally locally catenative formulas) underlie the structure of the Formulas for String Quartet of Tom Johnson.

Exactly learning automata with small cover time

Abstract: We present algorithms for exactly learning unknown environments that can be described by deterministic finite automata. The learner performs a walk on the target automaton, where at each step it observes the output of the state it is at, and chooses a labeled edge to traverse to the next state. The learner has no means of a reset, and does not have access to a teacher that answers equivalence queries and gives the learner counterexamples to its hypotheses. We present two algorithms: The first is for the case in which the outputs observed by the learner are always correct, and the second is for the case in which the outputs might be corrupted by random noise. The running times of both algorithms are polynomial in the cover time of the underlying graph of the target automaton.

Numerical evaluation of stochastic automata networks

Abstract: This paper examines some numerical issues in computing solutions to networks of stochastic automata. It is well-known that when the automata are completely independent, the cost of performing the operation basic to all iterative solution methods, that of matrix-vector multiply, is given by /spl rho//sub N/=/spl Pi//sub i=1//sup N/n/sub i//spl times//spl Sigma//sub i=1//sup N/n/sub i/, where n/sub i/ is the number of states in the i/sup th/ automaton and N is the number of automata in the network. We provide a number of lemmas that show that this relatively small number of operations is sufficient in many other cases in which the automata are not independent and we show how the automata should be ordered to achieve this. >

Self-Modifying Finite Automata - Power and Limitations

Abstract: The Self-Modifying Finite Automaton (SMFA) is a model of computation introduced in [RS93, RS94, RS95b]. Formal de nitions appear in [RS95a]. This paper further investigates the computational power of the model, and introduces the concepts of path determinism and register complexity.

On the potential use of cellular automata machines for electromagnetic field solution

Abstract: In this paper, the potential use of cellular automata machines for electromagnetic field solution is investigated. Cellular automata are computational models that operate on a discrete spatial lattice, evolve in discrete time, and employ simple discrete variables. We specifically examine the lattice gas automata which use simple variables to describe particles that interact with nearest neighbours on the lattice through simple rules. They are suitable for modelling the linear wave equation in two dimensions. A benefit of the cellular automata approach is that low-cost, special-purpose digital hardware exists for their efficient evaluation. The current state-of-the-art cellular automata machine is CAM-8. Computational experiments carried out on CAM-8 are provided for problems involving plane wave interaction with perfectly conducting and dielectric media in two dimensions. The examples indicate the potential use of lattice gas automata for modelling electromagnetics and their efficient evaluation using cellular automata machines.

Automata on infinite trees with counting constraints

Abstract: We investigate finite automata on infinite trees with the usual Muller criterion for the success of an infinite computation path, but with the acceptance paradigm modified in that not all the computation paths need to be successful. Instead, it is required that the number of successful paths must belong to a specified set of cardinals Γ. We show that Muller automata with the acceptance constraint of the form “there are at least γ accepting paths” can be always simulated by tree automata with a weaker criterion for successful paths, namely Buchi acceptance condition. We also show that this is the most general class of constraints for which a simulation by Buchi automata is always possible. Next, we characterize the maximal class of constraints which can be simulated by classical Muller automata (known to be more powerful than Buchi automata). The condition requiered of the set Γ there, is that the intersection with natural numbers forms a recognizable set. Finally, we exhibit a set of trees which is recognized by a classical Buchi automaton but fails to be recognized by any Muller automaton with a non trivial cardinality constraint (i.e., except for Γ = 0).

Determinizing Asynchronous Automata on Infinite Inputs

Abstract: Asynchronous automata are a natural distributed machine model for recognizing trace languages - languages defined over an alphabet equipped with an independence relation. To handle infinite traces, Gastin and Petit introduced Buchi asynchronous automata, which accept precisely the class of omega-regular trace languages. Like their sequential counterparts, these automata need to be non-deterministic in order to capture all omega-regular languages. Thus complementation of these automata is non-trivial. Complementation is an important operation because it is fundamental for treating the logical connective "not" in decision procedures for monadic second-order logics. Subsequently, Diekert and Muscholl solved the complementation problem by showing that with a Muller acceptance condition, deterministic automata suffice for recognizing omega-regular trace languages. However, a direct determinization procedure, extending the classical subset construction, has proved elusive. In this paper, we present a direct determinization procedure for Buchi asynchronous automata, which generalizes Safra's construction for sequential Buchi automata. As in the sequential case, the blow-up in the state space is essentially that of the underlying subset construction.

Finite State Automata and Connectionist Machines: A Survey

Abstract: Work in the literature related to Finite State Automata (FSAs) and Neural Networks (NNs) is review. These studies have dealt with Grammatical Inference tasks as well as how to represent FSAs through a neural model. The inference of Regular Grammars through NNs has been focused either on the acceptance or rejection of strings generated by the grammar or on the prediction of the possible successor(s) for each character in the string. Different neural architectures using first and second order connections were adopted. In order to extract the FSA inferred by a trained net, several techniques have been described in the literature, which are also reported here. Finally, theoretical work about the relationship between NNs and FSAs is outlined and discussed.

Smaller representations for finite-state transducers and finite-state automata

Abstract: Finite-state transducers and finite-state automata are efficient and natural representations for a large variety of problems. We describe a new algorithm for turning a finite-state transducer into the composition of two deterministic finite-state transducers such that the combined size of the derived transducers can be exponentially smaller than other known deterministic constructions. As a consequence, this can also be used to build deterministic representations of finite-state automata smaller than the minimal finite-state automata computed by the classic determinization and minimization algorithms. We also report experimental results on large scale dictionaries and rule-based systems.

Self-Modifying Finite Automata - Basic Definitions and Results

Abstract: We formally de ne the Self-Modifying Finite Automaton (SMFA), a model of computation introduced in [RS93, RS94, RS95], as a subclass of a new more general model, the Self-Modifying Automaton (SMA). SMAs are similar to standard nite automata, but changes to the transition set are allowed during a computation. An SMFA is constrained in that it can have only nitely many di erent modi cation instructions, and the e ect of each instruction must be computable.

A new type of pushdown automata on infinite trees

Abstract: In this paper we consider pushdown automata on infinite trees with empty stack as the accepting condition (ω-EPDTA). We provide the following regarding ω-EPDTA: (a) its relationship to other Pushdown automata on infinite trees, (b) a Kleene-Closure theorem and (c) a single exponential time algorithm for checking emptiness. We demonstrate the usefulness of ω-EPDTA through two example applications: defining the temporal uniform inevitability property and specifying a context-free process with unbounded state space, both of which cannot be defined and/or specified by the classical finite state automata on infinite trees. We also discuss the relevance of the results presented here to model-checking.

Logic Finite Automata

Abstract: A standard finite state automaton is an abstract machine which may take a finite number of states. Some states are marked as accepting states, and an initial state is specified in which the machine starts, faced with a word w over a finite input alphabet ∑. A finite transition table specifies the possibilities to change states, consuming a certain prefix of the actual rest of the input word. The automaton accepts a word if it is possible to eventually reach an accepting state with the empty word, choosing appropriate transitions.

Determinization of logical specifications of automata

Abstract: The present article is a continuation of a series of studies on functional synthesis of automata from their logical specifications. A specification language L based on the logic of one-place predicates interpreted on the set of integers has been described. A specification S in this language defines the class K(S) of equivalent nondeterministic automata. If S is treated as a specification of deterministic automata, then the class of all automata satisfying the specification S is identical with the class of all determinizations of any automaton from K(S). The problem of functional synthesis of a deterministic automaton specified in the language L involves constructing a procedural representation of the automaton (i.e., a representation in terms of states and transition and output functions) that satisfies the original specification. It thus includes the construction of one or several determinizations of an automaton from the class K(S). The last problem can be solved either on the procedural level (i.e., the level of the automaton graph) by constructing a procedural representation of an automation from K(S) or on the logical level (i.e., the level of formulas in the language L). In this article, we propose a solution of the problem based on the methodology ofmore » verification design of automaton. An essential feature of this methodology is that all transformations of the automaton being designed (except the construction of a procedural representation of the automaton) are carried out on the level of specification language formulas. This permits using logic methods to verify the correctness of the applied by the designer in the process of design. The problem is accordingly formulated as follows: given the specification S, constructed a specification S such that K(S{sup *}) is a class of equivalent deterministic automata that are determinizations of automata from K(S).« less

Hybrid Automata with Finite Mutual Simulations

Abstract: Many decidability results for hybrid automata rely upon the finite region bisimulation of timed automata [AD94]. Rectangular automata do not have finite bisimulations [Hen95], yet have many decidable verification problems [PV94,HKPV95]. We prove that every two-dimensional rectangular automaton A with positive-slope variables has a finite mutual simulation relation, which is the intersection of the region bisimulations defined by the extremal slopes of the variables of A. While the mutual simulation is infinite for two-dimensional automata with one variable taking both positive and negative slopes, it forms a regular tesselation of the plane, and therefore can be encoded by one counter. As a corollary, we obtain the decidability of model checking linear temporal logic on these automata.