Showing papers on "ω-automaton published in 2007"

Modal I/O automata for interface and product line theories

Abstract: Alfaro and Henzinger use alternating simulation in a two player game as a refinement for interface automata [1]. We show that interface automata correspond to a subset of modal transition systems of Larsen and Thomsen [2], on which alternating simulation coincides with modal refinement. As a consequence a more expressive interface theory may be built, by a simple generalization from interface automata to modal automata. We define modal I/O automata, an extension of interface automata with modality. Our interface theory that follows can express liveness properties, disallowing trivial implementations of interfaces, a problem that exists for theories build around simulation preorders. In order to further exemplify the usefulness of modal I/O automata, we construct a behavioral variability theory for product line development.

Modeling of discrete event systems using finite automata with variables

Abstract: To get industrial acceptance of supervisory control theory, there is a need to bridge the gap between the signal-based industrial reality and the event-based supervisory control framework. This paper tries to do this by introducing a modeling formalism with automata extended with variables, guard expressions and action functions. The formalism is suitable for modeling plants and specifications in the supervisory control framework. An algorithm that transforms a set of extended automata into a set of ordinary automata with equivalent behavior, is presented. This allows the user to model complex behaviors with a compact representation, and at the same time use existing algorithms for analysis.

Complementing two-way finite automata

Abstract: We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, for a given automaton (2dfa) with n states, we build an automaton accepting the complement with at most 4n states, independently of the size of the input alphabet. Actually, we show a stronger result, by presenting an equivalent 4n-state 2dfa that always halts. For the nondeterministic case, using a variant of inductive counting, we show that the complement of a unary language, accepted by an n-state two-way automaton (2nfa), can be accepted by an O(n^8)-state 2nfa. Here we also make 2nfa's halting. This allows the simulation of unary 2nfa's by probabilistic Las Vegas two-way automata with O(n^8) states.

Inapproximability of nondeterministic state and transition complexity assuming P ≠ NP

Abstract: Inapproximability results concerning minimization of nondeterministic finite automata relative to given deterministic finite automata were obtained only recently, modulo cryptographic assumptions [4]. Here we give upper and lower bounds on the approximability of this problem utilizing only the common assumption P ≠ NP, in the setup where the input is a finite language specified by a truth table. To this end, we derive an improved inapproximability result for the biclique edge cover problem. The obtained lower bounds on approximability can be sharpened in the case where the input is given as a deterministic finite automaton over a binary alphabet. This settles most of the open problems stated in [4]. Note that the biclique edge cover problem was recently studied by the authors as lower bound method for the nondeterministic state complexity of finite automata [5].

On 5' → 3' sensing Watson-Crick finite automata

Abstract: In this paper we introduce a variation of Watson-Crick automata in which both heads read the doubled DNA strand form 5' to 3'. The sensing version of these automata recognize exactly the linear context-free languages. The deterministic version is not so powerful, but all fixed-rated linear (for instance even-linear) languages can be accepted by them. Relation to other variations of Watson-Crick automata and pushdown automata are presented. The full-reading version of sensing 5′ → 3′ automata recognizes non context-free languages as well.

A characterization of regular expressions under bisimulation

Abstract: We solve an open question of Milner [1984]. We define a set of so-called well-behaved finite automata that, modulo bisimulation equivalence, corresponds exactly to the set of regular expressions, and we show how to determine whether a given finite automaton is in this set. As an application, we consider the star height problem.

On-the-fly stuttering in the construction of deterministic ω-automata

Abstract: We propose to use the knowledge that an ω-regular property is stutter insensitive to construct potentially smaller deterministic ω-automata for such a property, e.g. using Safra's determinization construction. This knowledge allows us to skip states that are redundant under stuttering, which can reduce the size of the generated automaton. In order to use this technique even for automata that are not completely insensitive to stuttering, we introduce the notion of partial stutter insensitiveness and apply our construction only on the subset of symbols for which stuttering is allowed. We evaluate the benefits of this heuristic in practice using multiple sets of benchmark formulas.

Improved algorithms for the automata-based approach to model-checking

Abstract: We propose and evaluate new algorithms to support the automata-based approach to model-checking: algorithms to solve the universality and language inclusion problems for nondeterministic Buchi automata. To obtain those new algorithms, we establish the existence of pre-orders that can be exploited to efficiently evaluate fixed points on the automata defined during the complementation step (that we keep implicit in our approach). We evaluate the performance of our new algorithm to check for universality of Buchi automata experimentally using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, our algorithm outperforms the standard ones by several orders of magnitude. This work is an extension to the infinite words case of new algorithms for the finite words case that we and co-authors have presented in a recent paper [DDHR06].

An algorithm for learning real-time automata

Abstract: We describe an algorithm for learning simple timed automata, known as real-time automata. The transitions of real-time automata can have a temporal constraint on the time of occurrence of the current symbol relative to the previous symbol. The learning algorithm is similar to the redblue fringe state-merging algorithm for the problem of learning deterministic finite automata. In addition to state merges, our algorithm can perform state splits by making use of the time values in the input data. We tested our learning algorithm on randomly generated problems. The results are promising and show that learning a real-time automaton directly from timed data outperforms a method that uses sampling in order to deal with the timed data.

Synchronizing automata preserving a chain of partial orders

Abstract: We present a new class of automata which strictly contains the class of aperiodic automata and shares with the latter certain synchronization properties. In particular, every strongly connected automaton in this new class is synchronizing and has a reset word of length ⌊n(n+1)/6⌋ where n is the number of states of the automaton.

Post-critically finite self-similar groups

Abstract: We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is contracting.

REGAL: a library to randomly and exhaustively generate automata

Abstract: The C++ library REGAL is devoted to the random and exhaustive generation of finite deterministic automata. The random generation of automata can be used for example to test properties of automata, to experimentally study average complexities of algorithms dealing with automata or to compare different implementations of the same algorithm. The exhaustive generation allows one to check conjectures on small automata.

Distributed time-asynchronous automata

Abstract: We show that the class of distributed time-asynchronous automata is more expressive than timed automata, has a decidable emptiness problem, is closed under union, concatenation, star, shuffle and renaming, but not under intersection. The closure results are obtained by showing that distributed time-asynchronous automata are equivalent with a subclass of shuffle regular expressions and its related class of stopwatch automata.

Mechanizing the powerset construction for restricted classes of ω-automata

Abstract: Automata over infinite words provide a powerful framework to solve various decision problems. However, the mechanized reasoning with restricted classes of automata over infinite words is often simpler and more efficient. For instance, weak deterministic Buchi automata (WDBAS) can be handled algorithmically almost as efficient as deterministic automata over finite words. In this paper, we show how and when the standard powerset construction for automata over finite words can be used to determinize automata over infinite words. An instance is the class of automata that accept WDBA-recognizable languages. Furthermore, we present applications of this new determinization construction. Namely, we apply it to improve the automata-based approach for the mixed firstorder linear arithmetic over the reals and the integers, and we utilize it to accelerate finite state model checking. We report on experimental results for these two applications.

Factor automata of automata and applications

Abstract: An efficient data structure for representing the full index of a set of strings is the factor automaton, the minimal deterministic automaton representing the set of all factors or substrings of these strings. This paper presents a novel analysis of the size of the factor automaton of an automaton, that is the minimal deterministic automaton accepting the set of factors of a finite set of strings, itself represented by a finite automaton. It shows that the factor automaton of a set of strings U has at most 2|Q| - 2 states, where Q is the number of nodes of a prefix-tree representing the strings in U, a bound that significantly improves over 2||U|| - 1, the bound given by Blumer et al. (1987), where ||U|| is the sum of the lengths of all strings in U. It also gives novel and general bounds for the size of the factor automaton of an automaton as a function of the size of the original automaton and the maximal length of a suffix shared by the strings it accepts. Our analysis suggests that the use of factor automata of automata can be practical for large-scale applications, a fact that is further supported by the results of our experiments applying factor automata to a music identification task with more than 15,000 songs.

Returning and non-returning parallel communicating finite automata are equivalent

Abstract: A parallel communicating automata system consists of several automata working independently in parallel and communicating with each other by request with the aim of recognizing a word. Rather surprisingly, returning parallel communicating finite automata systems are equivalent to the non-returning variants. We show this result by proving the equivalence of both with multihead finite automata. Some open problems are finally formulated.

Normalized expressions and finite automata

Abstract: There exist two well-known quotients of the position automaton of a regular expression. The first one, called the equation automaton, was first introduced by Mirkin from the notion of prebase and has been redefined by Antimirov from the notion of partial derivative. The second one, due to Ilie and Yu and called the follow automaton, can be obtained by eliminating e-transitions in an e-NFA that is always smaller than the classical e-NFAs (Thompson, Sippu and Soisalon–Soininen). Ilie and Yu discussed the difficulty of succeeding in a theoretical comparison between the size of the follow automaton and the size of the equation automaton and concluded that it is very likely necessary to realize experimental studies. In this paper we solve the theoretical question, by first defining a set of regular expressions, called normalized expressions, such that every regular expression can be normalized in linear time, and proving then that the equation automaton of a normalized expression is always smaller than its follow automaton.

An implementation of deterministic tree automata minimization

Abstract: A frontier-to-root deterministic finite-state tree automaton (DTA) can be used as a compact data structure to store collections of unranked ordered trees. DTAs are usually sparser than string automata, as most transitions are undefined and therefore, special care must be taken in order to minimize them efficiently. However, it is difficult to find simple and detailed descriptions of the minimization procedure in the published literature. Here, we fully describe a simple implementation of the standard minimization algorithm that needs a time in O(|A|2), with |A| being the size of the DTA.

Descriptional complexity of nondeterministic finite automata

Abstract: In this talk, I will survey recent results and discuss open problems on the state and transition complexity of nondeterministic finite automata.

State complexity of additive weighted finite automata

Abstract: It is known that the neighborhood of a regular language with respect to an additive distance is regular. We introduce an additive weighted finite automaton model that provides a conceptually simple way to reprove this result. We consider the state complexity of converting additive weighted finite automata to deterministic finite automata. As our main result we establish a tight upper bound for the state complexity of the conversion.

Automata and semigroups recognizing infinite words

Abstract: This paper is a survey on the algebraic approach to the theory of automata accepting infinite words We discuss the various acceptance modes (Buchi automata, Muller automata, transition automata, weak recognition by a finite semigroup, omega-semigroups) and prove their equivalence We also give two algebraic proofs of McNaughton's theorem on the equivalence between Buchi and Muller automata Finally, we present some recent work on prophetic automata and discuss its extension to transfinite words

Non-constructive methods for finite probabilistic automata

Abstract: Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.

Quantum logic and automata theory

Abstract: Publisher Summary It is noted that a theory of computation based on quantum logic is to be established as a logical foundation of quantum computation. Finite automata and pushdown automata are considered the simplest abstract mathematical models of computing machines. Automata theory is an essential part of computation theory. This chapter describes a systematic exposition of automata theory. In context to this theory, quantum logic is treated as an orthomodular lattice-valued logic. The approach employed in developing this theory is essentially the semantical analysis. This chapter introduces notions of orthomodular lattice-valued finite automata and pushdown automata and their various variants. It defines the classes of languages accepted—namely, orthomodular lattice-valued regular languages and context-free languages. This chapter also re-examines various properties of automata in the framework of quantum logic, including the Kleene theorem concerning equivalence between finite automata and regular expressions, equivalence between pushdown automata and context-free grammars, and the pumping lemma both for regular languages and for context-free languages.

Minimizing local automata

Abstract: We design an algorithm that minimizes irreducible deterministic local automata by a sequence of state mergings Two states can be merged if they have exactly the same outputs The running time of the algorithm is O(min(m(n-r+1), m log n)), where m is the number of edges, n the number of states of the automaton, and r the number of states of the minimized automaton In particular, the algorithm is linear when the automaton is already minimal and contrary to Hopcroft's minimization algorithm that has a O (kn log n) running time in this case, where k is the size of the alphabet, and that applies only to complete automata (Note that kn ges m) While Hopcroft's algorithm relies on a "negative strategy", starting from a partition with a single class of all states, and partitioning classes when it is discovered that two states cannot belong to the same class, our algorithm relies on a "positive strategy", starting from the trivial partition for which each class is a singleton Two classes are then merged when their leaders have the same outputs The algorithm applies to irreducible deterministic local automata, where all states are considered both initial and final These automata, also called covers, recognize symbolic dynamical shifts of finite type They serve to present a large class of constrained channels, the class of finite memory systems, used for channel coding purposes The algorithm also applies to irreducible deterministic automata that are left-closing and have a synchronizing word These automata present shifts that are called almost of finite type Almost-of-finite-type shifts make a meaningful class of shifts, intermediate between finite type shifts and sofic shifts

Restarting Tree Automata

Abstract: Restarting automata were introduced to model the linguistic concept of analysis by reduction. In recent years there was a growing effort to study classes of formal languages that are generated by different variants of these automata. We follow this line of research and generalize the model to a more complex data structure: free term algebras (or trees). Many of the known results about restarting automata on strings carry over to the new model. We study the expressive power of restarting tree automata and prove some closure properties.

On weighted büchi automata with order-complete weights

Abstract: We investigate Buchi automata with weights for the transitions. Assuming that the weights are taken in a suitable ordered semiring, we show how to define the behaviors of these automata on infinite words. Our main result shows that the formal power series arising in this way are precisely the ones which can be constructed using ω-rational operations. This extends the classical Kleene–Schutzenberger result for weighted finite automata to the case of infinite words and generalizes Buchi's theorem on languages of infinite words. We also derive versions of our main result for non-complete semirings and for other automata models.

Undecidability of universality for timed automata with minimal resources

Abstract: Timed automata were introduced by Alur and Dill in the early 1990s and have since become the most prominent modelling formalism for real-time systems. A fundamental limit to the algorithmic analysis of timed automata, however, results from the undecidability of the universality problem: does a given timed automaton accept every timed word? As a result, much research has focussed on attempting to circumvent this difficulty, often by restricting the class of automata under consideration, or by altering their semantics. In this paper, we study the decidability of universality for classes of timed automata with minimal resources. More precisely, we consider restrictions on the number of states and clock constants, as well as the size of the event alphabet. Our main result is that universality remains undecidable for timed automata with a single state, over a single-event alphabet, and using no more than three distinct clock constants.