Showing papers on "Automata theory published in 1998"

A unified framework for hybrid control: model and optimal control theory

Abstract: We propose a very general framework that systematizes the notion of a hybrid system, combining differential equations and automata, governed by a hybrid controller that issues continuous-variable commands and makes logical decisions. We first identify the phenomena that arise in real-world hybrid systems. Then, we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems, evolving on continuous-variable state spaces and subject to continuous controls and discrete transitions. The model captures the identified phenomena, subsumes previous models, yet retains enough structure to pose and solve meaningful control problems. We develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework. In particular, we demonstrate the existence of optimal (relaxed) and near-optimal (precise) controls and derive "generalized quasi-variational inequalities" that the associated value function satisfies. We summarize algorithms for solving these inequalities based on a generalized Bellman equation, impulse control, and linear programming.

Algorithmic analysis of nonlinear hybrid systems

Abstract: We present two methods for translating nonlinear hybrid systems into linear hybrid automata. Properties of the nonlinear systems can then be inferred from the automatic analysis of the translated linear hybrid automata. The first method, called clock translation, replaces constraints on nonlinear variables by constraints on clock variables. The second method, called linear phase-portrait approximation, conservatively overapproximates the phase portrait of a hybrid automaton using piecewise-constant polyhedral differential inclusions. Both methods are sound for safety properties. We illustrate both methods by using HYTECH, a symbolic model checker for linear hybrid automata, to automatically check properties of a nonlinear temperature controller and of a predator-prey ecology.

Efficient descriptor-vector multiplications in stochastic automata networks

Abstract: This paper examines numerical issues in computing solutions to networks of stochastic automata. It is well-known that when the matrices that represent the automata contain only constant values, the cost of performing the operation basic to all iterative solution methods, that of matrix-vector multiply, is given by ρN = ΠNi-1 ni × ΣNi=1 ni, where ni is the number of states in the ith automaton and N is the number of automata in the network. We introduce the concept of a generalized tensor product and prove a number of lemmas concerning this product. The result of these lemmas allows us to show that this relatively small number of operations is sufficient in many practical cases of interest in which the automata contain functional and not simply constant transitions. Furthermore, we show how the automata should be ordered to achieve this.

Multiple Counters Automata, Safety Analysis and Presburger Arithmetic

Abstract: We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form yi#yj + ci,j where yi is either xi or xi, the values of the counter i respectively after and before the transition, and # is any relational symbol in {=,≤,≥,>,<}. We show that the set of possible counter values which can be reached after any number of iterations of a loop is definable in the additive theory of ℕ (or ℤ or ℝ depending on the type of the counters). This result can be used for the safety analysis of multiple counters automata.

Automata and Coinduction (An Exercise in Coalgebra)

Abstract: The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the present treatment of automata theory may serve as an introduction to coalgebra.

Partial order reductions for timed systems

Abstract: In this paper, we present a partial-order reduction method for timed systems based on a local-time semantics for networks of timed automata. The main idea is to remove the implicit clock synchronization between processes in a network by letting local clocks in each process advance independently of clocks in other processes, and by requiring that two processes resynchronize their local time scales whenever they communicate. A symbolic version of this new semantics is developed in terms of predicate transformers, which enjoys the desired property that two predicate transformers are independent if they correspond to disjoint transitions in different processes. Thus we can apply standard partial order reduction techniques to the problem of checking reachability for timed systems, which avoid exploration of unnecessary interleavings of independent transitions. The price is that we must introduce extra machinery to perform the resynchronization operations on local clocks. Finally, we present a variant of DBM representation of symbolic states in the local time semantics for efficient implementation of our method.

Partial Order Reductions for Timed Systems

Abstract: In this paper, we present a partial-order reduction method for timed systems based on a local-time semantics for networks of timed automata. The main idea is to remove the implicit clock synchronization between processes in a network by letting local clocks in each process advance independently of clocks in other processes, and by requiring that two processes resynchronize their local time scales whenever they communicate. A symbolic version of this new semantics is developed in terms of predicate transformers, which enjoys the desired property that two predicate transformers are independent if they correspond to disjoint transitions in different processes. Thus we can apply standard partial order reduction techniques to the problem of checking reachability for timed systems, which avoid exploration of unnecessary interleavings of independent transitions. The price is that we must introduce extra machinery to perform the resynchronization operations on local clocks. Finally, we present a variant of DBM representation of symbolic states in the local time semantics for efficient implementation of our method.

Sur les automates circulaires et la conjecture de Černý

Abstract: A resect word takes all states of a finite automation to a single state Cerný conjectured that every n-state automaton admitting a reset word admits a short reset word, ie one of length at most (n - 1) 2 In this paper, we generalize our earliest result (the proof of the conjecture about biaised circular automata) to all circular automata

Modeling urgency in timed systems

Abstract: We define timed automata with deadlines (TAD) which are a class of timed automata where time progress conditions depend on deadlines associated with transitions. We show that using TAD makes urgency specification easier. We present the model of Petri nets with deadlines (PND), which are (1-safe) Petri nets extended with clocks exactly as TAD are extensions of automata. We compare PND with different classes of timed Petri nets (TPNs) and show that safe TPNs can be modeled as PND. Some applications to modeling systems and in particular to modeling multimedia documents are presented

On the Expressiveness of Real and Integer Arithmetic Automata (Extended Abstract)

Abstract: If read digit by digit, a n-dimensional vector of integers represented in base r can be viewed as a word over the alphabet r n . It has been known for some time that, under this encoding, the sets of integer vectors recognizable by finite automata are exactly those definable in Presburger arithmetic if independence with respect to the base is required, and those definable in a slight extension of Presburger arithmetic if only a specific base is considered.

Separating Exponentially Ambiguous Finite Automata from Polynomially Ambiguous Finite Automata

Abstract: We resolve an open problem raised by Ravikumar and Ibarra [SIAM J. Comput., 18 (1989), pp. 1263--1282] 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-letter 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.

The SHIFT programming language for dynamic networks of hybrid automata

Abstract: SHIFT is a programming language for describing and simulating dynamic networks of hybrid automata. Such systems consist of components which can be created, interconnected, and destroyed as the system evolves. Components exhibit hybrid behavior, e.g. continuous-time phases separated by instantaneous discrete-event transitions. Components may evolve independently, or they may interact through selected state variables and events. The interaction network itself may evolve. The SHIFT model and language were motivated by our need for tools that support dynamically reconfigurable hybrid systems. Our primary application is the specification and analysis of different designs for automatic control of vehicles and highway systems. From our previous experience in modeling, analysis, and implementation, we adopted the hybrid systems approach for modeling the system components. Since spatial relationships between vehicles change as they move, our application is characterized by a dynamically changing network of interactions between system components. SHIFT has also since been used in coordinated autonomous submarines, air traffic control systems, and material handling systems. We examine other work related to the SHIFT approach. In we describe the main features of the SHIFT language-states, inputs, outputs, differential equations, and algebraic definitions, discrete states, and state transitions. We give a simplified version of the SHIFT model. We discuss the models of a type, a component, and the world and give the formal semantics of the model.

Series-Parallel Posets: Algebra, Automata and Languages

Abstract: In order to model concurrency, we extend automata theory from the usual word languages (sets of labelled linear orders) to sets of labelled series-parallel posets - or, equivalently, to sets of terms in an algebra with two product operations: sequential and parallel. We first consider languages of posets having bounded width, and characterize them using depth-nilpotent algebras. Next we introduce series-rational expressions, a natural generalization of the usual rational expressions, as well as a notion of branching automaton. We show both a Myhill-Nerode theorem and a Kleene theorem. We also look at generalizations.

A comparison of Presburger engines for EFSM reachability

Abstract: Implicit state enumeration for extended finite state machines relies on a decision procedure for Presburger arithmetic. We compare the performance of two Presburger packages, the automata-based Shasta package and the polyhedrabased Omega package. While the raw speed of each of these two packages can be superior to the other by a factor of 50 or more, we found the asymptotic performance of Shasta to be equal or superior to that of Omega for the experiments we performed.

Relating Hierarchies of Word and Tree Automata

Abstract: For an ω-word language L, the derived tree language Path(L) is the language of trees having all their paths in L. We consider the hierarchies of deterministic automata on words and nondeterministic automata on trees with Rabin conditions in chain form. We show that L is on some level of the hierarchy of deterministic word automata iff Path(L) is on the same level of the hierarchy of nondeterministic tree automata.

A Comparison of Presburger Engines for EFSM Reachability

Abstract: Implicit state enumeration for extended finite state machines relies on a decision procedure for Presburger arithmetic. We compare the performance of two Presburger packages, the automata-based Shasta package and the polyhedrabased Omega package. While the raw speed of each of these two packages can be superior to the other by a factor of 50 or more, we found the asymptotic performance of Shasta to be equal or superior to that of Omega for the experiments we performed.

On the fly test generation for real time protocols

Abstract: Many critical, real-time systems or multimedia systems have time constraints in their specifications. But testing such systems isn't obvious, because the notion of time is not directly under control. A well known problem concerns explosion and complexity related to the computation of behavior graph for real time specifications. This paper introduces a novel approach aimed at avoiding explosion problems. Systems are modelled with timed input output automata. Starting with some formal protocol specification and some test purpose, a synchronous product is computed and a test sequence is generated on the fly, with the building of potential and success time intervals which are used to determine the result of the test: fail, pass or inconclusive.

Automatic Verification of a Lip-Synchronisation Protocol Using Uppaal

Abstract: We present the formal specification and verification of a lip-synchronisation protocol using the real-time model checker Uppaal. A number of specifications of this protocol can be found in the literature, but this is the first automatic verification. We take a published specification of the protocol, code it up in the Uppaal timed automata notation and then verify whether the protocol satisfies the key properties of jitter and skew. The verification reveals some aws in the protocol. In particular, it shows that for certain sound and video streams the protocol can time-lock before reaching a prescribed error state. We also discuss our experience with Uppaal, with particular reference to modelling timeouts and to deadlock analysis.

Regularity of solutions and homotopic equivalence for hybrid systems

Abstract: We study the trajectories of hybrid systems evolving according to constant, convex inclusions and Lipschitz nonlinear inclusions. Two questions are addressed. First, we investigate the existence of continuous selections of trajectories with respect to the initial conditions. Second, previous work on timed automata and hybrid automata has examined equivalence relations on runs of the automaton that visit the same locations and regions of the state space. Here we examine an equivalence relation defined directly on the trajectories. With suitable conditions on the enabling regions and using a suitable metric, we construct a homotopy on the set of solutions and use the homotopy to form an equivalence relation on the trajectories. We show the relationship between region equivalence introduced in Alur and Dill (1990) and homotopic equivalence. The tools needed for studying homotopic equivalence are the same as for obtaining continuity with respect to initial conditions.

Membership questions for timed and hybrid automata

Abstract: Timed and hybrid automata are extensions of finite state machines for formal modeling of embedded systems with both discrete and continuous components. Reachability problems for these automata are well studied and have been implemented in verification tools. For the purpose of effective error reporting and testing, we consider the membership problems for such automata. We consider different types of membership problems depending on whether the path (i.e. edge sequence), or the trace (i.e. event sequence), or the timed trace (i.e. timestamped event sequence), is specified. We give comprehensive results regarding the complexity of these membership questions for different types of automata, such as timed automata and linear hybrid automata, with and without /spl epsiv/ transitions. In particular we give an efficient O(n/spl middot/m/sup 2/) algorithm for generating timestamps corresponding to a path of length n in a timed automaton with m clocks. This algorithm is implemented in the verifier COSPAN to improve its diagnostic feedback during timing verification. Second, we show that for automata without /spl epsiv/ transitions, the membership question is NP complete for different types of automata whether or not the timestamps are specified along with the trace. Third, we show that for automata with /spl epsiv/ transitions, the membership question is as hard as the reachability question even for timed traces: it is PSPACE complete for timed automata, and undecidable for slight generalizations.

Controlled Timed Automata

Abstract: We examine some extensions of the basic model, due to Alur and Dill, of real-time automata (RTA) Our model, controlled real-time automata, is a parameterized family of real-time automata with some additional features like clock stopping, variable clock velocities and periodic tests We illustrate the power of controlled automata by presenting some languages that can be recognized deterministically by such automata, but cannot be recognized non-deterministically by any other previously introduced class of timed automata (even with ɛ-transitions) On the other hand, due to carefully chosen restrictions, controlled automata conserve basic properties of RTA: the emptiness problem is decidable and for each fixed parameter the family of recognized real-time languages is closed under boolean operations

Characterizing the Semantics of Terminological Cycles in ALN Using Finite Automata.

Abstract: Apparatus designed to measure, within a selectively variable defined range, the distance of an object's surface from opposite sides of a predetermined datum plane. The apparatus includes two pairs of light sources which are disposed on one side of the datum plane, and on opposite sides of a reflection viewing plane which is normal to the datum plane. In each source pair, the two sources are energized alternately to create, on opposite sides of the datum plane, and with regard to the viewing plane, alternate upper and lower preferential illumination zones. A photodetector, which "looks" for reflections along the viewing plane, has its output signal coordinately gated in such a manner that the level of such signal is directly interpretable to indicate the distance of a reflecting surface from the datum plane, as well as the side of such plane on which the surface is located.

On the language generated under fully decentralized supervision

Abstract: This paper studies the language generated under fully decentralized supervision proposed by Kozak and Wonham (1995). The author assumes that desirable behavior is specified as a closed language. A closed-form expression for the language generated under fully decentralized supervision is presented. It is shown that the generated language is larger than the supremal closed, controllable, and strongly decomposable sublanguage. Moreover, a necessary and sufficient condition is derived for the generated language to be the supremal closed and controllable sublanguage.

Optimizing tensor product computations in 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 optimizations related to the implementation of this algorithm. We also consider the possible benefits of grouping automata in a SAN with many small automata, to create an equivalent SAN having a smaller number of larger automata.

A Fast New Semi-incremental Algorithm for the Construction of Minimal Acyclic DFAs

Abstract: We present a semi-incremental algorithm for constructing minimal acyclic deterministic finite automata. Such automata are useful for storing sets of words for spell-checking, among other applications. The algorithm is semi-incremental because it maintains the automaton in near-minimal condition and requires a final minimization step after the last word has been added (during construction). The algorithm derivation proceeds formally (with correctness arguments) from two separate algorithms, one for minimization and one for adding words to acyclic automata. The algorithms are derived in such a way as to be combinable, yielding a semi-incremental one. In practice, the algorithm is both easy to implement and displays good running time performance.

Efficient encoding for exact symbolic automata-based scheduling

Abstract: This paper presents an efficient encoding and automaton construction which improves performance of automata-based scheduling techniques. The encoding preserves knowledge of what operations occurred previously but excludes when they occurred, allowing greater sharing among scheduling traces. The technique inherits all of the features of BDD-based control dominated scheduling including systematic speculation. Without conventional pruning, all schedules for several large samples are quickly constructed.

Multiple counters automata, safety analysis and presburger arithmetic

Abstract: We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j + C i,j where y i is either x' i or x i , the values of the counter i respectively after and before the transition, and # is any relational symbol in {=, ≤, ≥,>, <}. We show that the set of possible counter values which can be reached after any number of iterations of a loop is definable in the additive theory of N (or Z or R depending on the type of the counters). This result can be used for the safety analysis of multiple counters automata.