Showing papers on "ω-automaton published in 2005"

Safraless decision procedures

Abstract: The automata-theoretic approach is one of the most fundamental approaches to developing decision procedures in mathematical logics. To decide whether a formula in a logic with the tree-model property is satisfiable, one constructs an automaton that accepts all (or enough) tree models of the formula and then checks that the language of this automaton is nonempty. The standard approach translates formulas into alternating parity tree automata, which are then translated, via Safra's determinization construction, into nondeterministic parity automata. This approach is not amenable to implementation because of the difficulty of implementing Safra's construction and the nonemptiness test for nondeterministic parity tree automata. In this paper, we offer an alternative to the standard automata-theoretic approach. The crux of our approach is avoiding the use of Safra's construction and of nondeterministic parity tree automata. Our approach goes instead via universal co-Buchi tree automata and nondeterministic Buchi tree automata. Our translations are significantly simpler than the standard approach, less difficult to implement, and have practical advantages like being amenable to optimizations and a symbolic implementation. We also show that our approach yields better complexity bounds.

Distance desert automata and the star height problem

Abstract: We show that it is decidable in time complexity \(2^{2^{2^{O{(n)}}}}\) whether the language accepted by an n-state non-deterministic automaton is of star height one, which is the first ever complexity result for the star height one problem. To achieve this, we introduce distance desert automata as a joint generalization of distance automata and desert automata, and show the decidability of its limitedness problem by solving the underlying Burnside problem.

Automata and Square Complexes

Abstract: We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reprove the theorem of Macedonska, Nekrashevych, Sushchansky, on the connection between bi-reversible automata and the commensurator of a regular tree.

Perturbed timed automata

Abstract: We consider timed automata whose clocks are imperfect. For a given perturbation error 0

On-the-fly emptiness checks for generalized büchi automata

Abstract: Emptiness check is a key operation in the automata-theoretic approach to LTL verification. However, it is usually done on Buchi automata with a single acceptance condition. We review existing on-the-fly emptiness-check algorithms for generalized Buchi automata (i.e., with multiple acceptance conditions) and show how they compete favorably with emptiness-checks for degeneralized automata, especially in presence of weak fairness assumptions. We also introduce a new emptiness-check algorithm, some heuristics to improve existing checks, and propose algorithms to compute accepting runs in the case of multiple acceptance conditions.

An Introduction to Hybrid Automata

Abstract: ion methods are used to simplify models and make their analysis more tractable. Several equivalence relations have been studied for subclasses of hybrid systems. For example, it can be shown that transition systems of timed automata admit finite state abstractions, called region graphs, that are time-abstract bisimilar, see [7] for details. Those equivalence results are used to prove decidability of verification problems on subclasses of hybrid automata [26,32] and allow the use of well-known model-checking procedures that are guaranteed to terminate in the presence of finite quotients [35]. Other techniques that are not exact but use overapproximations have been proposed and have proven useful in practice: the approximation schema proposed in Section 4.3 is detailed and proven correct in [30]. Other interesting works about overapproximations can be found, among others, in [5, 9, 24]. 5.4 Control synthesis In this introduction, we have shown how we can model and verify controllers using hybrid automata. In our example, we have proposed a controller for the system and proven that the controller was correct for a list of requirements. A more ambitious goal than algorithmic (controller) verification is algorithmic (controller) synthesis. References about control synthesis include [14, 17, 31, 33,50]. 5.5 Semantics and robustness The semantics of hybrid automata that we defined in this chapter can be described as perfect. For example, it is possible to model, with this semantics, a controller that takes a given transition when a variable of the environment has exactly a given value. This can be considered as unrealistic because any implementation of such a controller will measure its environment through sensors that have finite precision. Alternative semantics that can be considered as robust are proposed in [11,22,23,37]. 5.6 Tool support and case studies Several tools for the automatic analysis of hybrid automata have been implemented. The tools Kronos [21] and Uppaal [16] can be used to analyze the subclass of timed automata. The tool HyTech [29] allows the analysis of linear hybrid automata. The tool CHARON [10] and the tool d/dt [12] allow the analysis of a more general class of hybrid automata.

Automata as abstractions

Abstract: We propose the use of tree automata as abstractions in the verification of branching time properties, and show several benefits. In this setting, soundness and completeness are trivial. It unifies the abundance of frameworks in the literature, and clarifies the role of concepts therein in terms of the well-studied field of automata theory. Moreover, using automata as models simplifies and generalizes results on maximal model theorems.

Minimizing tree automata for unranked trees

Abstract: Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. We start with the unranked tree automata (UTAs) that are standard in database theory, assuming bottom-up determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal UTAs in that class are not unique and that minimization is np-hard. We then study more recent automata classes that do allow for polynomial time minimization. Among those, we show that bottom-up deterministic stepwise tree automata yield the most succinct representations.

Removing bidirectionality from nondeterministic finite automata

Abstract: We prove that every two-way nondeterministic finite automaton with n states has an equivalent one-way nondeterministic finite automaton with at most ($^{2n}_{n+1}$) states. We also show this bound is exact.

The generalization of generalized automata: Expression automata

Abstract: We explore expression automata with respect to determinism and minimization. We define determinism of expression automata using prefix-freeness. This approach is, to some extent, similar to that of...

Techniques for scaling up analyses based on pre-interpretations

Abstract: Any finite tree automaton (or regular type) can be used to construct an abstract interpretation of a logic program, by first determinising and completing the automaton to get a pre-interpretation of the language of the program. This has been shown to be a flexible and practical approach to building a variety of analyses, both generic (such as mode analysis) and program-specific (with respect to a type describing some particular property of interest). Previous work demonstrated the approach using pre-interpretations over small domains. In this paper we present techniques that allow the method to be applied to more complex pre-interpretations and larger programs. There are two main techniques presented: the first is a novel algorithm for determinising finite tree automata, yielding a compact “product” form of the transitions of the result automaton, that is often orders of magnitude smaller than an explicit representation of the automaton. Secondly, it is shown how this form (which is a representation of a pre-interpretation) can then be input directly to a BDD-based analyser of Datalog programs. We demonstrate through experiments that much more complex analyses become feasible.

Closure properties of coalgebra automata

Abstract: We generalize some of the central results in automata theory to the abstraction level of coalgebras. In particular, we show that for any standard, weak pullback preserving functor F, the class of recognizable languages of F -coalgebras is closed under taking unions, intersections and projections. Our main technical result concerns a construction which transforms a given alternating F -automaton into an equivalent non-deterministic one.

A visual and interactive automata theory course emphasizing breadth of automata

Abstract: Teaching Theory of Computation and learning it are both challenging tasks. Moreover, students are not sufficiently interested/motivated to learn this material since: (i) they believe that the material is dated and of little use and (ii) it is too abstract and difficult. To counter the first perception, we have developed materials to illustrate the breadth of finite automata concepts. To overcome the second problem we have: enhanced and integrated visualization software and historical background into newly-devloped materials including homeworks and slides for lectures. Most of the materials are available at a web site for the course that we developed. Our preliminary experience is positive overall, but there are some remaining concerns.

Semi-Algebraic Constant Reset Hybrid Automata - SACoRe

Abstract: In this paper we introduce and study a special class of hybrid automata, Semi-Algebraic Constant Reset hybrid automata (SACoRe). SACoRe automata are an extension of Ominimal semi-algebraic automata over the reals in the case of flows obtained from non-autonomous systems of differential inclusions. Even though SACoRe automata do not have the finite bisimulation property, they do admit decision procedures for reachability and model checking for a limited fragment of CTL, by combining Tarski's decidability result over the reals and Michael's selection theorem.

Extended finite automata and word problems

Abstract: This paper considers extended finite automata over monoids, in the sense of Dassow and Mitrana. We show that the family of languages accepted by extended finite automata over a monoid K is controlled by the word problem of K in a precisely stated manner. We also point out a critical error in the proof of the main result in the paper by Dassow and Mitrana. However as one consequence of our approach, by analyzing a certain word problem, we obtain a complete proof of this result, namely that the family of languages accepted by extended finite automata over the free group of rank two is exactly the family of context-free languages. We further deduce that along with the free group of rank two, the only finitely generated groups with this property are precisely the groups that have a nonabelian free subgroup of finite index.

Rough finite-state automata

Abstract: The concept of a rough finite-state semi-automaton, in which the result of any transition is a rough set of states, is formulated and then extended to that of a rough finite-state automaton by adding the set of accepting states. The behavior of such an automaton is defined and turns out to be a rough set of input words.

Weak automata for the linear time µ-calculus

Abstract: This paper presents translations forth and back between formulas of the linear time μ-calculus and finite automata with a weak parity acceptance condition. This yields a normal form for these formulas, in fact showing that the linear time alternation hierarchy collapses at level 0 and not just at level 1 as known so far. The translation from formulas to automata can be optimised yielding automata whose size is only exponential in the alternation depth of the formula.

Modal strength reduction in quantified discrete duration calculus

Abstract: QDDC is a logic for specifying quantitative timing properties of reactive systems. An automata theoretic decision procedure for QDDC reduces each formula to a finite state automaton accepting precisely the models of the formula. This construction has been implemented into a validity/model checking tool for QDDC called DCVALID. Unfortunately, the size of the final automaton as well as the intermediate automata which are encountered in the construction can some times be prohibitively large. In this paper, we present some validity preserving transformations to QDDC formulae which result into more efficient construction of the formula automaton and hence reduce the validity checking time. The transformations can be computed in linear time. We provide a theoretical as well as an experimental analysis of the improvements in the formula automaton size and validity checking time due to our transformations.

Approximate recognition of non-regular languages by finite automata

Abstract: Approximate computation is a central concept in algorithms and computation theory Our notion of approximation is that the algorithm perform correctly on most of the inputs We propose some finite automata models to study the question of how well a finite automaton can approximately recognize a non-regular language On the one hand, we show that there are natural problems for which a DFA can correctly solve almost all the instances The design of these DFA's leads to a linear time randomized algorithm for approximate integer multiplication On the other hand, we show that some languages (such as Lmajority = {x ∈ (0 + 1)* | x has more 1's than 0's}) can't be approximated by any regular language in a strong sense We also present results comparing different models of approximation

Improve capability of DNA automaton: DNA automaton with three internal states and tape head move in two directions

Abstract: DNA automaton is a simple molecular-scale automaton, in which the converting of information deploys in molecule-scale by DNA and DNA-manipulating enzymes autonomously Finite automaton with two internal states has been applied to medical diagnosis This paper analyses the computation ability of DNA automaton with different enzymes and the possibility of DNA finite automaton with three internal states which is more powerful than the two internal states finite automaton Finally, we describe a DNA finite automaton with three internal states and proposal a scheme of DNA automaton model in which the tape head can move forward and backward, and symbols can be read from and write into the tape, thus extend the computation ability of DNA automaton and its application fields

Cycle structure in automata and the holonomy decomposition

Abstract: The algebraic hierarchical decomposition of finite state automata can be applied wherever a finite system should be 'understood' using a hierarchical coordinate system. Here we use the holonomy decomposition for characterizing finite automata using derived hierarchical structure. This leads to a characterization according to the existence of different cycles within an automaton. The investigation shows that the problem of determining holonomy groups can be reduced to the examination of the cycle structure of certain derived automata. The results presented here lead to the improvements of the decomposition algorithms bringing closer the possibility of the application of the cascaded decomposition for real-world problems.

Reordering finite automata states for fast string recognition

Abstract: The spatial and temporal locality of reference on which cache memory relies to minimize cache swaps, is exploited to design a new algorithm for finite automaton string recognition. It is shown that the algorithm, referred to as the state reordering algorithm, outperforms the traditional table-driven algorithm for strings that tend to repeatedly access the same set of states.

Similarity relations and cover automata

Abstract: Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate consequences.