Showing papers on "ω-automaton published in 2012"

Introduction To Automata Theory, Languages And Computation, 3Rd Edition

Abstract: G' A. Linz, Peter. An introduction to formal languages and automata / Peter Linz'--3'd cd charrgcs ftrr the second edition wercl t)volutionary rather than rcvolrrtionary and addressed Initially, I felt that giving solutions to exercises was undesirable hecause it lirrritcd the Chapter 1 fntroduction to the Theory of Computation. Issuu solution manual to introduction to languages. Introduction theory computation 2nd edition solution manual sipser. Structural Theory of automata: solution manual of theory of computation. Kellison theory of interest pdf. Transformation, Sylvester's theorem(without proof), Solution of Second Order. Linear Differential Higher Engineering Mathematics by B.S. Grewal, 40th Edition, Khanna. Publication. 2. Introduction Of Automata Theory, Languages and computationHopcroft. Motwani&Ulman UNIX system Utilities manual. 4.

LTL to büchi automata translation: fast and more deterministic

Abstract: We introduce improvements in the algorithm by Gastin and Oddoux translating LTL formulae into Buchi automata via very weak alternating co-Buchi automata and generalized Buchi automata. Several improvements are based on specific properties of any formula where each branch of its syntax tree contains at least one eventually operator and at least one always operator. These changes usually result in faster translations and smaller automata. Other improvements reduce non-determinism in the produced automata. In fact, we modified all the steps of the original algorithm and its implementation known as LTL2BA. Experimental results show that our modifications are real improvements. Their implementations within an LTL2BA translation made LTL2BA very competitive with the current version of SPOT, sometimes outperforming it substantially.

Inferring canonical register automata

Abstract: In this paper, we present an extension of active automata learning to register automata , an automaton model which is capable of expressing the influence of data on control flow. Register automata operate on an infinite data domain, whose values can be assigned to registers and compared for equality. Our active learning algorithm is unique in that it directly infers the effect of data values on control flow as part of the learning process. This effect is expressed by means of registers and guarded transitions in the resulting register automata models. The application of our algorithm to a small example indicates the impact of learning register automata models: Not only are the inferred models much more expressive than finite state machines, but the prototype implementation also drastically outperforms the classic L * algorithm, even when exploiting optimal data abstraction and symmetry reduction.

Jumping finite automata

Abstract: The present paper proposes a new investigation area in automata theory — jumping finite automata. These automata work like classical finite automata except that they read input words discontinuously — that is, after reading a symbol, they can jump over some symbols within the words and continue their computation from there. The paper establishes several results concerning jumping finite automata in terms of commonly investigated areas of automata theory, such as decidability and closure properties. Most importantly, it achieves several results that demonstrate differences between jumping finite automata and classical finite automata. In its conclusion, the paper formulates several open problems and suggests future investigation areas.

One-Way Finite Automata with Quantum and Classical States

Abstract: In this paper, we introduce and explore a new model of quantum finite automata (QFA). Namely, one-way finite automata with quantum and classical states (1QCFA), a one way version of two-way finite automata with quantum and classical states (2QCFA) introduced by Ambainis and Watrous in 2002 [3]. First, we prove that coin-tossing one-way probabilistic finite automata (coin-tossing 1PFA) [23] and one-way quantum finite automata with control language (1QFACL) [6] as well as several other models of QFA, can be simulated by 1QCFA. Afterwards, we explore several closure properties for the family of languages accepted by 1QCFA. Finally, the state complexity of 1QCFA is explored and the main succinctness result is derived. Namely, for any prime m and any e1 > 0, there exists a language L m that cannot be recognized by any measure-many one-way quantum finite automata (MM-1QFA) [12] with bounded error \(\frac{7}{9}+\epsilon_1\), and any 1PFA recognizing it has at last m states, but L m can be recognized by a 1QCFA for any error bound e > 0 with O(logm) quantum states and 12 classical states.

Deciding the Value 1 Problem for Probabilistic Leaktight Automata

Abstract: The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton, are there words accepted with probability arbitrarily close to 1? This problem was proved undecidable recently. We sharpen this result, showing that the undecidability holds even if the probabilistic automata have only one probabilistic transition. Our main contribution is to introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is shown decidable (and PSPACE-complete). We construct an algorithm based on the computation of a monoid abstracting the behaviors of the automaton, and rely on algebraic techniques developed by Simon for the correctness proof. The class of leaktight automata is decidable in PSPACE, subsumes all subclasses of probabilistic automata whose value 1 problem is known to be decidable (in particular deterministic automata), and is closed under two natural composition operators.

Handbook of Finite State Based Models and Applications

Abstract: Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. Handbook of Finite State Based Models and Applications provides a complete collection of introductory materials on finite state theories, algorithms, and the latest domain applications. For beginners, the book is a handy reference for quickly looking up model details. For more experienced researchers, it is suitable as a source of in-depth study in this area. The book first introduces the fundamentals of automata theory, including regular expressions, as well as widely used automata, such as transducers, tree automata, quantum automata, and timed automata. It then presents algorithms for the minimization and incremental construction of finite automata and describes Esterel, an automata-based synchronous programming language for embedded system software development. Moving on to applications, the book explores regular path queries on graph-structured data, timed automata in model checking security protocols, pattern matching, compiler design, and XML processing. It also covers other finite state-based modeling approaches and applications, including Petri nets, statecharts, temporal logic, and UML state machine diagrams.

On the complexity of minimizing probabilistic and quantum automata

Abstract: Several types of automata, such as probabilistic and quantum automata, require to work with real and complex numbers. For such automata the acceptance of an input is quantified with a probability. There are plenty of results in the literature addressing the complexity of checking the equivalence of these automata, that is, checking whether two automata accept all inputs with the same probability. On the other hand, the critical problem of finding the minimal automata equivalent to a given one has been left open [C. Moore, J.P. Crutchfield, Quantum automata and quantum grammars, Theoret. Comput. Sci. 237 (2000) 275-306, see p. 304, Problem 5]. In this work, we reduce the minimization problem of probabilistic and quantum automata to finding a solution of a system of algebraic polynomial (in)equations. An EXPSPACE upper bound on the complexity of the minimization problem is derived by applying [email protected]?s algorithm. More specifically, we show that the state minimization of probabilistic automata, measure-once quantum automata, measure-many quantum automata, measure-once generalized quantum automata, and measure-many generalized quantum automata is decidable and in EXPSPACE. Finally, we also solve an open problem concerning minimal covering of stochastic sequential machines [A. Paz, Introduction to Probabilistic Automata, Academic Press, New York, 1971, p. 43].

Symbolic automata: the toolkit

Abstract: The symbolic automata toolkit lifts classical automata analysis to work modulo rich alphabet theories. It uses the power of state-of-the-art constraint solvers for automata analysis that is both expressive and efficient, even for automata over large finite alphabets. The toolkit supports analysis of finite symbolic automata and transducers over strings. It also handles transducers with registers. Constraint solving is used when composing and minimizing automata, and a much deeper and powerful integration is also obtained by internalizing automata as theories. The toolkit, freely available from Microsoft Research, has recently been used in the context of web security for analysis of potentially malicious data over Unicode characters.

Automata finiteness criterion in terms of van der Put series of automata functions

Abstract: In the paper we develop the p-adic theory of discrete automata. Every automaton \(\mathfrak{A}\) (transducer) whose input/output alphabets consist of p symbols can be associated to a continuous (in fact, 1-Lipschitz) map from p-adic integers to p-adic integers, the automaton function \(f_\mathfrak{A} \). The p-adic theory (in particular, the p-adic ergodic theory) turned out to be very efficient in a study of properties of automata expressed via properties of automata functions. In the paper we prove a criterion for finiteness of the number of states of automaton in terms of van der Put series of the automaton function. The criterion displays connections between p-adic analysis and the theory of automata sequences.

Quantitative languages defined by functional automata

Abstract: A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs. On the positive side, we show that functionality is decidable for the four measures. Furthermore, the existential and universal threshold problems, the language inclusion problem and the equivalence problem are all decidable when the weighted automata are functional. On the negative side, we also study the quantitative extension of the realizability problem and show that it is undecidable for sum, mean and ratio. We finally show how to decide whether the language associated with a given functional automaton can be defined with a deterministic one, for sum, mean and discounted sum. The results on functionality and determinizability are expressed for the more general class of functional weighted automata over groups. This allows one to formulate within the same framework new results related to discounted sum automata and known results on sum and mean automata. Ratio automata do not fit within this general scheme and specific techniques are required to decide functionality.

Multi-Core Reachability for Timed Automata

Abstract: Model checking of timed automata is a widely used technique. But in order to take advantage of modern hardware, the algorithms need to be parallelized. We present a multi-core reachability algorithm for the more general class of well-structured transition systems, and an implementation for timed automata. Our implementation extends the opaal tool to generate a timed automaton successor generator in c++, that is efficient enough to compete with the uppaal model checker, and can be used by the discrete model checker LTSmin, whose parallel reachability algorithms are now extended to handle subsumption of semi-symbolic states. The reuse of efficient lockless data structures guarantees high scalability and efficient memory use. With experiments we show that opaal+LTSmin can outperform the current state-of-the-art, uppaal. The added parallelism is shown to reduce verification times from minutes to mere seconds with speedups of up to 40 on a 48-core machine. Finally, strict BFS and (surprisingly) parallel DFS search order are shown to reduce the state count, and improve speedups.

Forms of Determinism for Automata (Invited Talk)

Abstract: We survey in this paper some variants of the notion of determinism, refining the spectrum between non-determinism and determinism. We present unambiguous automata, strongly unambiguous automata, prophetic automata, guidable automata, and history-deterministic automata. We instantiate these various notions for finite words, infinite words, finite trees, infinite trees, data languages, and cost functions. The main results are underlined and some open problems proposed.

Finite-State Automata on Infinite Inputs.

Abstract: This paper is a self-contained introduction to the theory of finite-state automata on infinite words The study of automata on infinite inputs was initiated by Buchi in order to settle certain decision problems arising in logic Subsequently, there has been a lot of fundamental work in this area, resulting in a rich and elegant mathematical theory In recent years, there has been renewed interest in these automata because of the fundamental role they play in the automatic verification of finite-state systems

Synchronization of automata with one undefined or ambiguous transition

Abstract: We consider the careful synchronization of partial automata with only one undefined transition and the generalized synchronization of nondeterministic automata with only one ambiguous transition. For each of the two cases we prove that the problem of checking whether or not a given automaton is synchronizable is PSPACE-complete. The restrictions of these problems to 2-letter automata are also PSPACE-complete.

Superiority of one-way and realtime quantum machines∗∗∗

Abstract: In automata theory, quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to QFAs augmented with counters or stacks. In this paper, we focus on such generalizations of QFAs where the input head operates in one-way or realtime mode, and present some new results regarding their superiority over their classical counterparts. Our first result is about the nondeterministic acceptance mode: Each quantum model architecturally intermediate between realtime finite state automaton and one-way pushdown automaton (one-way finite automaton, realtime and one-way finite automata with one-counter, and realtime pushdown automaton) is superior to its classical counterpart. The second and third results are about bounded error language recognition: for any k > 0, QFAs with k blind counters outperform their deterministic counterparts; and, a one-way QFA with a single head recognizes an infinite family of languages, which can be recognized by one-way probabilistic finite automata with at least two heads. Lastly, we compare the nondeterminictic and deterministic acceptance modes for classical finite automata with k blind counter(s), and we show that for any k > 0, the nondeterministic models outperform the deterministic ones.

Forms of Determinism for Automata

Abstract: We survey in this paper some variants of the notion of determinism, refining the spectrum between non-determinism and determinism. We present unambiguous automata, strongly unambiguous automata, prophetic automata, guidable automata, and history-deterministic automata. We instantiate these various notions for finite words, infinite words, finite trees, infinite trees, data languages, and cost functions. The main results are underlined and some open problems proposed. 1998 ACM Subject Classification F.1.1 Models of Computation, F.1.2 Modes of Computation, F.4.3 Formal Languages

Distribution of the number of accessible states in a random deterministic automaton

Abstract: We study the distribution of the number of accessible states in deterministic and complete automata with n states over a k-letters alphabet. We show that as n tends to infinity and for a fixed alphabet size, the distribution converges in law toward a Gaussian centered around vkn and of standard deviation equivalent to k p n, for some explicit constants vk and k. Using this characterization, we give a simple algorithm for random uniform generation of accessible deterministic and complete automata of size n of expected complexity O(n p n), which matches the best methods known so far. Moreover, if we allow a " variation around n in the size of the output automaton, our algorithm is the first solution of linear expected complexity. Finally we show how this work can be used to study accessible automata (which are dicult to apprehend from a combinatorial point of view) through the prism of the simpler deterministic and complete automata. As an example, we show how the average complexity inO(n log logn) for Moore’s minimization algorithm obtained by David for deterministic and complete automata can be extended to accessible automata. 1998 ACM Subject Classification F.2 Analysis of algorithms and problem complexity

One-Way Reversible Multi-head Finite Automata

Abstract: One-way multi-head finite automata are considered towards their ability to perform reversible computations. It is shown that, for every number k ≥ 1 of heads, there are problems which can be solved by one-way k-head finite automata, but not by any one-way reversible k-head finite automaton. Additionally, a proper head hierarchy is obtained for one-way reversible multi-head finite automata. Finally, decidability problems are considered. It turns out that one-way reversible finite automata with two heads are still a powerful model, since almost all commonly studied problems are not even semidecidable.

Forest automata for verification of heap manipulation

Abstract: We consider verification of programs manipulating dynamic linked data structures such as various forms of singly and doubly-linked lists or trees. We consider important properties for this kind of systems like no null-pointer dereferences, absence of garbage, shape properties, etc. We develop a verification method based on a novel use of tree automata to represent heap configurations. A heap is split into several "separated" parts such that each of them can be represented by a tree automaton. The automata can refer to each other allowing the different parts of the heaps to mutually refer to their boundaries. Moreover, we allow for a hierarchical representation of heaps by allowing alphabets of the tree automata to contain other, nested tree automata. Program instructions can be easily encoded as operations on our representation structure. This allows verification of programs based on symbolic state-space exploration together with refinable abstraction within the so-called abstract regular tree model checking. A motivation for the approach is to combine advantages of automata-based approaches (higher generality and flexibility of the abstraction) with some advantages of separation-logic-based approaches (efficiency). We have implemented our approach and tested it successfully on multiple non-trivial case studies.

OpenNWA: a nested-word automaton library

Abstract: Nested-word automata (NWAs) are a language formalism that helps bridge the gap between finite-state automata and pushdown automata. NWAs can express some context-free properties, such as parenthesis matching, yet retain all the desirable closure characteristics of finite-state automata. This paper describes OpenNWA, a C++ library for working with NWAs. The library provides the expected automata-theoretic operations, such as intersection, determinization, and complementation. It is packaged with WALi--the Weighted Automaton Library--and interoperates closely with the weighted pushdown system portions of WALi.

Almost-Sure Model-Checking of Reactive Timed Automata

Abstract: We consider the model of stochastic timed automata, a model in which both delays and discrete choices are made probabilistically. We are interested in the almost-sure model-checking problem, which asks whether the automaton satisfies a given property with probability 1. While this problem was shown decidable for single-clock automata few years ago, it was also proven that the algorithm for this decidability result could not be used for general timed automata. In this paper we describe the subclass of reactive timed automata, and we prove decidability of the almost-sure model-checking problem under that restriction. Decidability relies on the fact that this model is almost-surely fair. As a desirable property of real systems, we show that reactive automata are almost-surely non-Zeno. Finally we show that the almost-sure model-checking problem can be decided for specifications given as deterministic timed automata.

Feasible automata for two-variable logic with successor on data words

Abstract: We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data automata. It is strictly less expressive than data automata and the expressive power is incomparable with register automata. The expressive power of weak data automata corresponds exactly to existential monadic second order logic with successor +1 and data value equality ˜, EMSO2(+1,˜). It follows from previous work, David, et. al. in 2010, that the nonemptiness problem for weak data automata can be decided in 2-NEXPTIME. Furthermore, we study weak Buchi automata on data ω-strings. They can be characterized by the extension of EMSO2(+1,˜) with existential quantifiers for infinite sets. Finally, the same complexity bound for its nonemptiness problem is established by a nondeterministic polynomial time reduction to the nonemptiness problem of weak data automata.