Showing papers on "Automata theory published in 2000"
TL;DR: It is proved through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems, and practical numerical tests based on mixed-integer linear programming are proposed.
Abstract: We prove, in a constructive way, the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics, automata, and propositional logic. By focusing our investigation on the former class, we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems. Instead, we propose practical numerical tests based on mixed-integer linear programming.
678 citations
01 Jul 2000
TL;DR: This work presents a method to design controllers for safety specifications in hybrid systems, using analysis based on optimal control and game theory for automata and continuous dynamical systems to derive Hamilton-Jacobi equations whose solutions describe the boundaries of reachable sets.
Abstract: We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and discrete control and disturbance parameters. We translate safety specifications into restrictions on the system's reachable sets of states. Then, using analysis based on optimal control and game theory for automata and continuous dynamical systems, we derive Hamilton-Jacobi equations whose solutions describe the boundaries of reachable sets. These equations are the heart of our general controller synthesis technique for hybrid systems, in which we calculate feedback control laws for the continuous and discrete variables, which guarantee that the hybrid system remains in the "safe subset" of the reachable set. We discuss issues related to computing solutions to Hamilton-Jacobi equations. Throughout, we demonstrate out techniques on examples of hybrid automata modeling aircraft conflict resolution, autopilot flight mode switching, and vehicle collision avoidance.
571 citations
TL;DR: This work proposes quantum versions of finite-state and push-down automata, and regular and context-free grammars, and finds analogs of several classical theorems, including pumping lemmas, closure properties, rational and algebraic generating functions, and Greibach normal form.
398 citations
Proceedings Article•
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26 Jun 2000
TL;DR: This work determines the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic and gives model-theoretic characterisations for automatic structures via interpretations.
Abstract: We study definability and complexity issues for automatic and /spl omega/-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for extending many algorithmic and logical methods from finite structures to infinite ones. We explain the notion of (/spl omega/-)automatic structures, give examples, and discuss the relationship to automatic groups. We determine the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic. Further we study closure properties and definability issues on automatic structures and present a technique for proving that a structure is not automatic. We give model-theoretic characterisations for automatic structures via interpretations. Finally we discuss the composition theory of automatic structures and prove that they are closed under finitary Feferman-Vaught-like products.
365 citations
22 Aug 2000
TL;DR: The expressive power of this class of automata is investigated, and it is shown that any finite or infinite timed language accepted by a linear hybrid automaton is also acceptable by a stopwatch automaton.
Abstract: In this paper we define and study the class of stopwatch automata which are timed automata augmented with stopwatches and unobservable behaviour. In particular, we investigate the expressive power of this class of automata, and show as a main result that any finite or infinite timed language accepted by a linear hybrid automaton is also acceptable by a stopwatch automaton. The consequences of this result are two-fold: firstly, it shows that the seemingly minor upgrade from timed automata to stopwatch automata immediately yields the full expressive power of linear hybrid automata. Secondly, reachability analysis of linear hybrid automata may effectively be reduced to reachability analysis of stopwatch automata. This, in turn, may be carried out using an easy (over-approximating) extension of the efficient reachability analysis for timed automata to stopwatch automata. We report on preliminary experiments on analyzing translations of linear hybrid automata using a stopwatch-extension of the real-time verification tool UPPAAL.
230 citations
25 Jan 2000
TL;DR: The SASI approach to enforcing security policies by modifying object code for a target system before that system is executed has been prototyped for two different machine architectures: Intel x86 and Java JVML.
Abstract: SASI (Security Automata SFI Implementation) enforces security policies by modifying object code for a target system before that system is executed. The approach has been prototyped for two rather different machine architectures: Intel x86 and Java JVML. Details of these prototypes and some generalizations about the SASI approach are discussed.
206 citations
TL;DR: It is shown that templates are able to model timed languages corresponding to single and multiple-instance behaviors and combinations thereof, and can thus represent languages that could not be represented or monitored using timed automata alone.
Abstract: This paper introduces a new framework for modeling discrete event processes. This framework, called condition templates, allows the modeling of processes in which both single-instance and multiple-instance behaviors are exhibited concurrently. A single-instance behavior corresponds to a trace from a single finite-state process, and a multiple-instance behavior corresponds to the timed interleavings of an unspecified number of identical processes operating at the same time. The template framework allows the modeling of correct operation for systems consisting of concurrent mixtures of both single and multiple-instance behaviors. This representation can then be used in online fault monitoring for confirming the correct operation of a system. We compare the class of timed languages representable by template models with classes of timed languages from timed automata models. It is shown that templates are able to model timed languages corresponding to single and multiple-instance behaviors and combinations thereof. Templates can thus represent languages that could not be represented or monitored using timed automata alone.
136 citations
TL;DR: A new simple algorithm for learning multiplicity automata with improved time and query complexity is presented, and the learnability of various concept classes is proved, including the class of disjoint DNF and more generally satisfy-O(1) DNF.
Abstract: We study the learnability of multiplicity automata in Angluin's exact learning model, and we investigate its applications. Our starting point is a known theorem from automata theory relating the number of states in a minimal multiplicity automaton for a function to the rank of its Hankel matrix. With this theorem in hand, we present a new simple algorithm for learning multiplicity automata with improved time and query complexity, and we prove the learnability of various concept classes. These include (among others): -The class of disjoint DNF, and more generally satisfy-O(1) DNF. -The class of polynomials over finite fields. -The class of bounded-degree polynomials over infinite fields. -The class of XOR of terms. -Certain classes of boxes in high dimensions. In addition, we obtain the best query complexity for several classes known to be learnable by other methods such as decision trees and polynomials over GF(2).While multiplicity automata are shown to be useful to prove the learnability of some subclasses of DNF formulae and various other classes, we study the limitations of this method. We prove that this method cannot be used to resolve the learnability of some other open problems such as the learnability of general DNF formulas or even k-term DNF for k = o(log n) or satisfy-s DNF formulas for s = o(1). These results are proven by exhibiting functions in the above classes that require multiplicity automata with super-polynomial number of states.
127 citations
TL;DR: The algebraic properties of the set of series–parallel posets are used to investigate the notion of recognizability, based on finite-index congruences, and a notion of regularity based on a new class of “branching” automata.
121 citations
25 Mar 2000
TL;DR: This paper presents an overview of algorithms for constructing automata from linear arithmetic constraints and identifies one case in which the special structure of the automata that are constructed allows a linear-time determinization procedure to be used.
Abstract: This paper presents an overview of algorithms for constructing automata from linear arithmetic constraints. It identifies one case in which the special structure of the automata that are constructed allows a linear-time determinization procedure to be used. Furthermore, it shows through theoretical analysis and experiments that the special structure of the constructed automata does, in quite a general way, render the usual upper bounds on automata operations vastly overpessimistic.
113 citations
23 Mar 2000
TL;DR: It is shown that the existence of a Zeno run is Σ11 -complete for semi-linear hybrid automata; it is too complex to be expressed in first-order arithmetic.
Abstract: We define a new class of hybrid automata for which reachability is decidable--a proper superclass of the initialized rectangular hybrid automata--by taking parallel compositions of simple components. Attempting to generalize, we encounter timed automata with algebraic constants. We show that reachability is undecidable for these algebraic timed automata by simulating two-counter Minsky machines. Modifying the construction to apply to parametric timed automata, we reprove the undecidability of the emptiness problem, and then distinguish the dense and discrete-time cases with a new result. The algorithmic complexity-- both classical and parametric--of one-clock parametric timed automata is also examined. We finish with a table of computability-theoretic complexity results, including that the existence of a Zeno run is Σ11 -complete for semi-linear hybrid automata; it is too complex to be expressed in first-order arithmetic.
20 Sep 2000
TL;DR: This work presents a variant of hybrid automata augmented with discrete probability distributions, and focuses on restricted subclasses of the model in order to obtain decidable model checking algorithms for properties expressed in probabilistic temporal logics.
Abstract: Hybrid automata offer a framework for the description of systems with both discrete and continuous components, such as digital technology embedded in an analogue environment. Traditional uses of hybrid automata express choice of transitions purely in terms of nondeterminism, abstracting potentially significant information concerning the relative likelihood of certain behaviours. To model such probabilistic information, we present a variant of hybrid automata augmented with discrete probability distributions. We concentrate on restricted subclasses of the model in order to obtain decidable model checking algorithms for properties expressed in probabilistic temporal logics.
27 Sep 2000
TL;DR: A conservative extension to traditional nondeterministic finite automata (NFAs) is proposed to keep track of the positions in the input string for the last uses of selected transitions, by adding "tags" to transitions.
Abstract: A conservative extension to traditional nondeterministic finite automata (NFAs) is proposed to keep track of the positions in the input string for the last uses of selected transitions, by adding "tags" to transitions. The resulting automata are reminiscent of nondeterministic Mealy machines. A formal semantics of automata with tagged transitions is given. An algorithm is given to convert these augmented automata to the corresponding deterministic automata, which can be used to process strings efficiently. The application to regular expressions is discussed, explaining how the algorithms can be used to implement, for example, substring addressing and a lookahead operator, and an informal comparison to other widely-used algorithms is made.
01 Jan 2000
TL;DR: This case study illustrates how verification can be performed directly on a model of the hybrid system dynamics without first constructing an approximation to the continuous dynamics using timed automata or linear hybrid automata models.
Abstract: We present a formal verification of a control algorithm from the literature for a four-cylinder four-stroke engine in the cutoff mode. The controlled system is modeled, simulated and verified using CheckMate, a tool for formal verification of hybrid systems developed at Carnegie Mellon University. CheckMate automatically constructs a polyhedral-invariant hybrid automaton (PIHA) from a Matlab/Simulink model of the hybrid system and performs the verification using discrete model approximations. This case study illustrates how verification can be performed directly on a model of the hybrid system dynamics without first constructing an approximation to the continuous dynamics using timed automata or linear hybrid automata models.
TL;DR: It is shown that any CLDA can be reduced to a linear discrete-time system with periodic coefficients, and called a CLDA globally stable if it has a periodic trajectory which attracts all other trajectories of the system.
TL;DR: The main contribution of this paper is to introduce automata equivalent to PSTs but having the following properties: Learning the automaton, for any L, takes O (n) time, and prediction of a string of m symbols by the Automaton takes O(m) time.
Abstract: Statistical modeling of sequences is a central paradigm of machine learning that finds multiple uses in computational molecular biology and many other domains. The probabilistic automata typically built in these contexts are subtended by uniform, fixed-memory Markov models. In practice, such automata tend to be unnecessarily bulky and computationally imposing both during their synthesis and use. Recently, D. Ron, Y. Singer, and N. Tishby built much more compact, tree-shaped variants of probabilistic automata under the assumption of an underlying Markov process of variable memory length. These variants, called Probabilistic Suffix Trees (PSTs) were subsequently adapted by G. Bejerano and G. Yona and applied successfully to learning and prediction of protein families. The process of learning the automaton from a given training set S of sequences requires theta(Ln2) worst-case time, where n is the total length of the sequences in S and L is the length of a longest substring of S to be considered for a candidate state in the automaton. Once the automaton is built, predicting the likelihood of a query sequence of m characters may cost time theta(m2) in the worst case. The main contribution of this paper is to introduce automata equivalent to PSTs but having the following properties: Learning the automaton, for any L, takes O (n) time. Prediction of a string of m symbols by the automaton takes O (m) time. Along the way, the paper presents an evolving learning scheme and addresses notions of empirical probability and related efficient computation, which is a by-product possibly of more general interest.
TL;DR: The pumping lemma in automata theory based on quantum logic is established and the equivalence between the recognizabilty by the product and union of orthomodular lattice-valued automata is shown to be equivalent to the distributivity of meet over union in the truth-value set.
Abstract: We establish the pumping lemma in automata theory based on quantum logicunder certain conditions on implication, and discuss the recognizability by theproduct and union of orthomodular lattice-valued (quantum) automata. Inparticular, we show that the equivalence between the recognizabilty by the productof automata and the conjunction of the recognizabilities by the factor automatais equivalent to the distributivity of meet over union in the truth-value set.
26 Jun 2000
TL;DR: A refinement of the theory of well quasi-orderings is demonstrated to be more appropriate for symbolic model checking, since it allows inventing constraint systems which are both well semi-ordered and compact.
Abstract: Many existing algorithms for model checking of infinite-state systems operate on constraints which are used to represent (potentially infinite) sets of states. A general powerful technique which can be employed for proving termination of these algorithms is that of well quasi-orderings. Several methodologies have been proposed for derivation of new well quasi-ordered constraint systems. However, many of these constraint systems suffer from a "constraint explosion problem", as the number of the generated constraints grows exponentially with the size of the problem. We demonstrate that a refinement of the theory of well quasi-orderings, called the theory of better quasi-orderings is more appropriate for symbolic model checking, since it allows inventing constraint systems which are both well quasi-ordered and compact. We apply our methodology to derive new constraint systems for verification of systems with unboundedly many clocks, broadcast protocols, lossy channel systems, and integral relational automata. The new constraint systems are exponentially more succinct than existing ones, and their well quasi-ordering cannot be shown by previous methods in the literature.
01 Nov 2000
TL;DR: This paper focuses on the model-based diagnosis of a class of distributed discrete-event systems, called active systems, and features a problem-decomposition/solution-composition nature whose core is the online progressive reconstruction of the behavior of the active system, guided by the available observations.
Abstract: Discrete-event modeling can be applied to a large variety of physical systems, in order to support different tasks, including fault detection, monitoring, and diagnosis. The paper focuses on the model-based diagnosis of a class of distributed discrete-event systems, called active systems. An active system, which is designed to react to possibly harmful external events, is modeled as a network of communicating automata, where each automaton describes the behavior of a system component. Unlike other approaches based on the synchronous composition of automata and on the off-line creation of the model of the entire system, the proposed diagnostic technique deals with asynchronous events and does not need any global diagnoser to be built. Instead, the current approach features a problem-decomposition/solution-composition nature whose core is the online progressive reconstruction of the behavior of the active system, guided by the available observations. This incremental technique makes effective the diagnosis of large-scale active systems, for which the one-shot generation of the global model is almost invariably impossible in practice. The diagnostic method encompasses three steps: (1) reconstruction planning; (2) behavior reconstruction; and (3) diagnosis generation. Step 1 draws a hierarchical decomposition of the behavior reconstruction problem. Reconstruction is made in Step 2, where an intensional representation of all the dynamic behaviors which are consistent with the available system observation is produced. Diagnosis is eventually generated in Step 3, based on the faulty evolutions incorporated within the reconstructed behaviors. The modular approach is formally defined, with special emphasis on Steps 2 and 3, and applied to the power transmission network domain.
19 Jun 2000
TL;DR: The authors present a method for automatic verification of real time control programs running on LEGO RCX TM bricks using the verification tool UPPAAL, and have constructed, modeled and verified a machine for sorting LEGO bricks by color.
Abstract: The authors present a method for automatic verification of real time control programs running on LEGO RCX TM bricks using the verification tool UPPAAL. The control programs, consisting of a number of tasks running concurrently, are automatically translated into the timed automata model of UPPAAL. The fixed scheduling algorithm used by the LEGO RCXTM processor is modeled in UPPAAL, and supply of similar (sufficient) timed automata models for the environment allows analysis of the overall real time system using the tools of UPPAAL. To illustrate our techniques, we have constructed, modeled and verified a machine for sorting LEGO bricks by color.
TL;DR: The specification discloses wheel and axle assemblies in each of which a sealing washer serves both as a bearing seal and a thrust washer.
01 Mar 2000
TL;DR: This paper describes how to increase the visualization and interaction in the automata theory course through the use of the tools JFLAP and Pâté and describes new features in these tools that allow additional visualize and interaction.
Abstract: In this paper we describe how to increase the visualization and interaction in the automata theory course through the use of the tools JFLAP and Pâte. We also describe new features in these tools that allow additional visualization and interaction. New features in JFLAP include the addition of regular expressions and exploring their conversion from and to nondeterministic finite automata (NFA), and increasing the interaction in the conversion of automata to grammars. New features in Pâte include the display of a parse tree while parsing unrestricted grammars, and improved interaction with parsing and the transformation of grammars.
TL;DR: This work shows that H is pure (that is, closed under radical) if and only if Synt(H) is aperiodic, and shows that testing for this property of H is PSPACE-complete.
25 Nov 2000
TL;DR: This paper introduces the notion of quantum pushdown automata (QPA) in a non-equivalent way, including unitarity criteria, by using the definition of quantum finite automata of [11] and shows that QPA can recognize every regular language.
Abstract: Quantum finite automata, as well as quantum pushdown automata were first introduced by C. Moore, J. P. Crutchfield [13]. In this paper we introduce the notion of quantum pushdown automata (QPA) in a non-equivalent way, including unitarity criteria, by using the definition of quantum finite automata of [11]. It is established that the unitarity criteria of QPA are not equivalent to the corresponding unitarity criteria of quantum Turing machines [4]. We show that QPA can recognize every regular language. Finally we present some simple languages recognized by QPA, two of them are not recognizable by deterministic pushdown automata and one seems to be not recognizable by probabilistic pushdown automata as well.
Journal Article•
11 Sep 2000
TL;DR: It is shown that DeLeTe can produce the canonical RFSA of a regular language L from any sample S which contains S L and a learning algorithm (DeLeTe) is defined.
Abstract: We define here the Residual Finite State Automata class (RFSA). This class, included in the Non deterministic Finite Automata class, strictly contains the Deterministic Finite Automata class and shares with it a fundamental property : the existence of a canonical minimal form for any regular language. We also define a notion of characteristic sample S L for a given regular language L and a learning algorithm (DeLeTe). We show that DeLeTe can produce the canonical RFSA of a regular language L from any sample S which contains S L . We think that working on non deterministic automata will allow, in a great amount of cases, to reduce the size of the characteristic sample. This is already true for some languages for which the sample needed by DeLete is far smaller than the one needed by classical algorithms.
TL;DR: It is shown that this game for checking the nonemptiness of HAA, generalises the nested depth-first algorithm used to check the nonemption of nondeterministic Büchi automata (used in Spin).
Abstract: We describe an efficient CTL* model checking algorithm based on alternating automata and games. A CTL* formula, expressing a correctness property, is first translated to a hesitant alternating automaton and then composed with a Kripke structure representing the model to be checked, after which this resulting automaton is then checked for nonemptiness. We introduce the nonemptiness game that checks the nonemptiness of a hesitant alternating automaton (HAA). In the same way that alternating automata generalise nondeterministic automata, we show that this game for checking the nonemptiness of HAA, generalises the nested depth-first algorithm used to check the nonemptiness of nondeterministic Buchi automata (used in Spin).
27 Nov 2000
TL;DR: Presents a computational framework based on tabled resolution and constraint processing for verifying real-time systems and discusses the implementation of this framework in the context of the XMC/RT (eXtended Model Checker/Real-Time) verification tool.
Abstract: Presents a computational framework based on tabled resolution and constraint processing for verifying real-time systems. We also discuss the implementation of this framework in the context of the XMC/RT (eXtended Model Checker/Real-Time) verification tool. For systems specified using timed automata, XMC/RT offers backward and forward reachability analysis, as well as timed modal mu-calculus model checking. It can also handle timed infinite-state systems, such as those with unbounded message buffers, provided the set of reachable states is finite. We illustrate this capability on a real-time version of the Leader Election protocol. Finally, XMC/RT can function as a model checker for untimed systems. Despite this versatility, preliminary benchmarking experiments indicate that XMC/RT's performance remains competitive with that of other real-time verification tools.
TL;DR: The notion of asynchronous mapping introduced by Cori, Metivier and Zielonka is generalized to pomsets and it is shown how to construct a deterministic ACA~from an asynchronous mapping and the relation between the expressiveness of monadic second-order logic, nondeterministic ACAs and deterministic ACA is investigated.