Showing papers on "ω-automaton published in 2000"

Efficient Büchi automata from LTL formulae

Abstract: We present an algorithm to generate small Buchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure, and simplification of the resulting automaton. We present a translation procedure that is optimal within a certain class of translation procedures. The simplification algorithm can be used for Buchi automata in general. It reduces the number of states and transitions, as well as the number and size of the accepting sets-possibly reducing the strength of the resulting automaton. This leads to more efficient model checking of linear-time logic formulae. We compare our method to previous work, and show that it is significantly more efficient for both random formulae, and formulae in common use and from the literature.

Efficient Büchi Automata from LTL Formulae

Abstract: We present an algorithm to generate small Buchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure, and simplification of the resulting automaton. We present a translation procedure that is optimal within a certain class of translation procedures. The simplification algorithm can be used for Buchi automata in general. It reduces the number of states and transitions, as well as the number and size of the accepting sets—possibly reducing the strength of the resulting automaton. This leads to more efficient model checking of linear-time logic formulae. We compare our method to previous work, and show that it is significantly more efficient for both random formulae, and formulae in common use and from the literature.

The Impressive Power of Stopwatches

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.

Incremental construction of minimal acyclic finite-state automata

Abstract: In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite-state automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it. Our approach is to construct a minimal automaton in a single phase by adding new strings one by one and minimizing the resulting automaton on-the-fly. We present a general algorithm as well as a specialization that relies upon the lexicographical ordering of the input strings. Our method is fast and significantly lowers memory requirements in comparison to other methods.

On the Construction of Automata from Linear Arithmetic Constraints

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.

Decidability and Complexity Results for Timed Automata and Semi-linear Hybrid Automata

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.

An automata-theoretic approach to reasoning about infinite-state systems

Abstract: We develop an automata-theoretic framework for reasoning about infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way tree automaton that navigates through the tree. As has been the case with finite-state systems, the automata-theoretic framework is quite versatile. We demonstrate it by solving several versions of the model-checking problem for μ-calculus specifications and prefix-recognizable systems, and by solving the realizability and synthesis problems for μ-calculus specifications with respect to prefix-recognizable environments.

NFAs with tagged transitions, their conversion to deterministic automata and application to regular expressions

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.

Automata Theory Based on Quantum Logic II

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.

Effective control synthesis for DES under partial observations

Abstract: A procedure is given for the effective solution of an infinite-string supervisory control problem under partial observations, for the case where the plant and specification languages are represented by finite /spl omega/-automata (automata on infinite strings), and the observation mask by a finite Moore automaton. This solves an /spl omega/-language version of the standard centralized supervisory control problem under partial observations. It is shown that a natural extension to decentralized control is undecidable, even if the plant, the specification languages and the masks are represented by finite automata. This undecidability result carries over to the finite-string case.

Optimal amnesic probabilistic automata or how to learn and classify proteins in linear time and space

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. In [8], much more compact, tree-shaped variants of probabilistic automata are built which assume an underlying Markov process of variable memory length. In [3, 4], these variants, called Probabilistic Suffix Trees (PSTs) were successfully applied to learning and prediction of protein families. The process of learning the automaton from a given training set S of sequences requires Θ (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 Θ (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 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 sheme, and addresses notions of empirical probability and related efficient computation,possibly a by-product of more general interest.

Timed automata with periodic clock constraints

Abstract: The traditional constraints on the clocks of a timed automaton are based on real intervals, e. g., the value of a clock belongs to the interval (0; 1). Here, we introduce a new set of constraints, which we call \\periodic\", and which are based on regularly repeated real intervals, e. g., the value modulo 2 of a clock belongs to the interval (0; 1) which means that it belongs to (0; 1) or (2; 3) or (4; 5) .. .. Automata with these new constraints have greater expressive power than the au-tomata with traditional sets while satissability remains decidable. We address questions concerning-moves: simulation of automata with periodic constraints by au-tomata with traditional constraints and removal of-moves under certain conditions. Then, we enrich our model by introducing \\count-down\" clocks and show that the expressive power is not increased. Finally, we study three special cases: 1) all transitions reset clocks, 2) no transition reset clocks, and 3) the time domain is discrete and prove the decidability of the inclusion problem under each of these hypotheses.

Increasing visualization and interaction in the automata theory course

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.

Expressiveness of Updatable Timed Automata

Abstract: Since their introduction by Alur and Dill, timed automata have been one of the most widely studied models for real-time systems. The syntactic extension of so-called updatable timed automata allows more powerful updates of clocks than the reset operation proposed in the original model. We prove that any language accepted by an updatable timed automaton (from classes where emptiness is decidable) is also accepted by a "classical" timed automaton. We propose even more precise results on bisimilarity between updatable and classical timed automata.

Learning Regular Languages Using Non Deterministic Finite Automata

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.

Constructively formalizing automata theory

Abstract: Adhesive dressing compositions are disclosed which are useful in restoring and improving adhesive joint surfaces such as grout surfaces in ceramic tile installations by easy, efficient methods. Such compositions form stain resistant, water repellent, washable coverings which adhere to most adhesive surfaces and further have properties of preferential adherability to certain adhesive surfaces compared with adjacent adherend surfaces. The compositions comprise a polymer in the form of an emulsion, an alkali-thickenable polymer, an alkaline material and water with other components including pigments, plasticizers and solvents.

On the Complexity of Bisimulation Problems for Pushdown Automata

Abstract: All bisimulation problems for pushdown automata are at least PSPACE-hard. In particular, we show that (1) Weak bisimilarity of pushdown automata and finite automata is PSPACE-hard, even for a small fixed finite automaton, (2) Strong bisimilarity of pushdown automata and finite automata is PSPACE-hard, but polynomial for every fixed finite automaton, (3) Regularity (finiteness) of pushdown automata w.r.t. weak and strong bisimilarity is PSPACE-hard.

Finite automata over free groups

Abstract: Finite automata are extended by adding an element of a given group to each of their configurations. An input string is accepted if and only if the neutral element of the group is associated to a final configuration reached by the automaton. We get a new characterization of the context-free languages as soon as the considered group is the binary free group. The result cannot be carried out in the deterministic case. Some remarks about finite automata over other groups are also presented.

Context-Free Recognition with Weighted Automata

Abstract: We introduce the definition of language recognition with weighted automata, a generalization of the classical definition of recognition with unweighted acceptors. We show that, with our definition of recognition, weighted automata can be used to recognize a class of languages that strictly includes regular languages. The class of languages accepted depends on the weight set which has the algebraic structure of a semiring. We give a generic linear time algorithm for recognition with weighted automata and describe examples with various weight sets illustrating the recognition of several classes of context-free languages. We prove, in particular, that the class of languages equivalent to the language of palindromes can be recognized by weighted automata over the (+,ċ)-semiring, and that the class of languages equivalent to the Dyck language of first order D 1 '*can be recognized by weighted automata over the real tropical semiring. We also prove that weighted automata over the real tropical semiring can be used to recognize regular expressions.

Model-Checking for Hybrid Systems by Quotienting and Constraints Solving

Abstract: In this paper we present a semi-algorithm to do compositional model-checking for hybrid systems. We first define a modal logic \(L_{ u}^h\) which is expressively complete for linear hybrid automata. We then show that it is possible to extend the result on compositional model-checking for parallel compositions of finite automata and networks of timed automata to linear hybrid automata. Finally we present some results obtained with an extension of the tool CMC to handle a subclass of hybrid automata (the stopwatch automata).

Automata-based symbolic scheduling

Abstract: This dissertation presents a set of techniques for representing the high-level b ior of a digital subsystem as a collection of nondeterministic finite automata, N Desired behavioral and implementation dynamics: dependencies, repet bounded resources, sequential character, and control state, can also be sim modeled. All possible system execution sequences, obeying imposed constr are encapsulated in a composed NFA. Technology similar to that used in sym model checking enables implicit exploration and extraction of best-possible ex tion sequences. This provides a very general, systematic procedure to pe exact high-level synthesis of cyclic, control-dominated behaviors constraine arbitrary sequential constraints. This dissertation further demonstrates that techniques are scalable to practical problem sizes and complexities. Exact sch ing solutions are constructed for a variety of academic and industrial proble including a pipelined RISC processor. The ability to represent and sche sequential models with hundreds of tasks and one-half million control cases stantially raises the bar as to what is believed possible for exact scheduling mo

Measures of Nondeterminism in Finite Automata

Abstract: While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem area is the study of different measures of nondeterminism in finite automata. Our results are: 1. There is an exponential gap in the number of states between unambiguous nfa's and general nfa's. Moreover, deterministic communication complexity provides lower bounds on the size of unambiguous nfa's. 2. For an nfa A we consider the complexity measures adviceA(n) as the number of advice bits, ambigA(n) as the number of accepting computations, and lea fA(n) as the number of computations for worst case inputs of size n. These measures are correlated as follows (assuming that the nfa A has at most one "terminally rejecting" state): adviceA(n); ambigA(n) ≤ leafA(n) ≤ O(adviceA(n) ċ ambigA(n)). 3. leafA(n) is always either a constant, between linear and polynomial in n, or exponential in n. 4. There is a language for which there is an exponential size gap between nfa's with exponential leaf number/ambiguity and nfa's with polynomial leaf number/ambiguity. There also is a family of languages KONm2 such that there is an exponential size gap between nfa's with polynomial leaf number/ambiguity and nfa's with ambiguity m.

Experiments with Automata Compression

Abstract: Several compression methods of finite-state automata are presented and evaluated. Most compression methods used here are already described in the literature. However, their impact on the size of automata has not been described yet. We fill that gap, presenting results of experiments carried out on automata representing German, and Dutch morphological dictionaries.

An Automata-Based Recognition Algorithm for Semi-extended Regular Expressions

Abstract: This paper is concerned with the recognition problem for semi-extended regular expressions: given a semi-extended regular expression r of length m and an input string x of length n, determine if x ∈ L(r), where L(r) denotes the language denoted by r. Although the recognition algorithm based on nondeterministic finite automata (NFAs) for regular expressions is widely known, a similar algorithm based on finite automata is currently not known for semi-extended regular expressions. The existing algorithm is based on dynamic programming. We here present an efficient automata-based recognition algorithm by introducing a new model of alternating finite automata called partially input-synchronized alternating finite automata (PISAFAs for short). Our algorithm based on PISAFAs runs in O(mn2) time and O(mn + kn2) space, though the existing algorithm based on dynamic programming runs in O(mn3) time and O(mn2) space, where k is the number of intersection operators occurring in r. Thus our algorithm significantly improves the existing one.

Once more about the state-minimization of the nondeterministic finite automata

Abstract: In this paper we consider the corrected version of the algorithm of the state-minimization for the nondeterministic finite automata: we correct here a mistake of the previous paper, where the same problem was considered.