Showing papers on "Pushdown automaton published in 2014"

Automata and Computability

Abstract: From the Publisher: This introduction to the basic theoretical models of computability develops their rich and varied structure. The first part is devoted to finite automata and their properties. Afterwards, pushdown automata are utilized as a broader class of models, enabling the analysis of context-free languages. In the remaining chapters, Turing machines are introduced, and the book culminates in discussions of effective computability, decidability, and Godel's incompleteness theorems.

From LTL to Deterministic Automata: A Safraless Compositional Approach

Abstract: We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula i¾?. The automaton is the product of a master automaton and an array of slave automata, one for each G-subformula of i¾?. The slave automaton for G i¾? is in charge of recognizing whether FG i¾? holds. As opposed to standard determinization procedures, the states of all our automata have a clear logical structure, which allows for various optimizations. Our construction subsumes former algorithms for fragments of LTL. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.

Complexity of input-driven pushdown automata

Abstract: In an input-driven pushdown automaton (IDPDA), the current input symbol determines whether the automaton performs a push operation, a pop operation, or does not touch the stack. Inputdriven pushdown automata, also known under alternative names of visibly pushdown automata and of nested word automata, have been intensively studied because of their desirable features: for instance, the model allows determinization, and the associated family of languages retains many of the strong closure and decidability properties of regular languages. This paper reports on various aspects of the complexity of input-driven pushdown automata, such as their descriptional complexity, the computational complexity of their membership problem and of other decision problems for input-driven languages. The research on IDPDAs has been associated to their complexity from the very beginning. When Mehlhorn [25] originally introduced the model, it was studied as a subclass of deterministic context-free languages with better space complexity. Further work on the model carried out in the 1980s [6, 12, 36] concentrated on improving the bounds on the complexity of the languages accepted by such automata, culminating in the proof of their containment in NC1. In 2004, the model was reintroduced by Alur and Madhusudan [2] under the name of visibly pushdown automata, and among their most important contributions were the first results on the descriptional complexity of the model, such as upper and lower bounds on the number of states in automata representing some operations on languages. Also, Alur and Madhusudan [2] established the computational complexity of several decision problems for the model. The paper by Alur and Madhusudan [2] sparked a renewed interest in IDPDAs, and inspired the research on various aspects of the model [1, 8, 10, 19, 39]. Alur and Madhusudan [3] also introduced an equivalent outlook on IDPDAs as automata operating on nested words, which provide a natural model for applications such as XML document processing, where data has a dual linear-hierarchical structure. Nested word automata have been studied in a number of recent papers [9, 11, 17, 35, 37]. Another equivalent outlook on IDPDAs is represented by pushdown forest automata [14], that are, roughly speaking, tree walking automata that traverse the tree in depth-first left-to-right order and are equipped with a synchronized pushdown.

Pushdown automata in statistical machine translation

Abstract: This article describes the use of pushdown automata (PDA) in the context of statistical machine translation and alignment under a synchronous context-free grammar. We use PDAs to compactly represent the space of candidate translations generated by the grammar when applied to an input sentence. General-purpose PDA algorithms for replacement, composition, shortest path, and expansion are presented. We describe HiPDT, a hierarchical phrase-based decoder using the PDA representation and these algorithms. We contrast the complexity of this decoder with a decoder based on a finite state automata representation, showing that PDAs provide a more suitable framework to achieve exact decoding for larger synchronous context-free grammars and smaller language models. We assess this experimentally on a large-scale Chinese-to-English alignment and translation task. In translation, we propose a two-pass decoding strategy involving a weaker language model in the first-pass to address the results of PDA complexity analysis. We study in depth the experimental conditions and tradeoffs in which HiPDT can achieve state-of-the-art performance for large-scale SMT.

Aspects of Reversibility for Classical Automata

Abstract: Some aspects of logical reversibility for computing devices with a finite number of discrete internal states are addressed. These devices have a read-only input tape, may be equipped with further resources, and evolve in discrete time. The reversibility of a computation means in essence that every configuration has a unique successor configuration and a unique predecessor configuration. The notion of reversibility is discussed. In which way is the predecessor configuration computed? May we use a universal device? Do we have to use a device of the same type? Or else a device with the same computational power? Do we have to consider all possible configurations as potential predecessors? Or only configurations that are reachable from some initial configurations? We present some selected aspects as gradual reversibility and time-symmetry as well as results on the computational capacity and decidability mainly of finite automata and pushdown automata, and draw attention to the overall picture and some of the main ideas involved.

Hyper-Ackermannian bounds for pushdown vector addition systems

Abstract: This paper studies the boundedness and termination problems for vector addition systems equipped with one stack. We introduce an algorithm, inspired by the Karp & Miller algorithm, that solves both problems for the larger class of well-structured pushdown systems. We show that the worst-case running time of this algorithm is hyper-Ackermannian for pushdown vector addition systems. For the upper bound, we introduce the notion of bad nested words over a well-quasi-ordered set, and we provide a general scheme of induction for bounding their lengths. We derive from this scheme a hyper-Ackermannian upper bound for the length of bad nested words over vectors of natural numbers. For the lower bound, we exhibit a family of pushdown vector addition systems with finite but large reachability sets (hyper-Ackermannian).

Scope-Bounded Pushdown Languages

Abstract: We study the formal language theory of multistack pushdown automata (Mpa) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded number of contexts of S (scoped Mpa) We contribute to show that scoped Mpa are indeed a robust model of computation, by focusing on the corresponding theory of visibly Mpa (Mvpa) We prove the equivalence of the deterministic and nondeterministic versions and show that scope-bounded computations of an n-stack Mvpa can be simulated, rearranging the input word, by using only one stack These results have several interesting consequences, such as, the closure under complement, the decidability of universality, inclusion and equality, and a Parikh theorem We also give a logical characterization and compare the expressiveness of the scope-bounded restriction with Mvpa classes from the literature

Reservoir Computing using Cellular Automata.

Abstract: We introduce a novel framework of reservoir computing Cellular automaton is used as the reservoir of dynamical systems Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir The proposed framework is capable of long short-term memory and it requires orders of magnitude less computation compared to Echo State Networks Also, for additive cellular automaton rules, reservoir features can be combined using Boolean operations, which provides a direct way for concept building and symbolic processing, and it is much more efficient compared to state-of-the-art approaches

Symbolic Visibly Pushdown Automata

Abstract: Nested words model data with both linear and hierarchical structure such as XML documents and program traces. A nested word is a sequence of positions together with a matching relation that connects open tags (calls) with the corresponding close tags (returns). Visibly Pushdown Automata are a restricted class of pushdown automata that process nested words, and have many appealing theoretical properties such as closure under Boolean operations and decidable equivalence. However, like any classical automata models, they are limited to finite alphabets. This limitation is restrictive for practical applications to both XML processing and program trace analysis, where values for individual symbols are usually drawn from an unbounded domain. With this motivation, we introduce Symbolic Visibly Pushdown Automata (SVPA) as an executable model for nested words over infinite alphabets. In this model, transitions are labeled with predicates over the input alphabet, analogous to symbolic automata processing strings over infinite alphabets. A key novelty of SVPAs is the use of binary predicates to model relations between open and close tags in a nested word. We show how SVPAs still enjoy the decidability and closure properties of Visibly Pushdown Automata. We use SVPAs to model XML validation policies and program properties that are not naturally expressible with previous formalisms and provide experimental results for our implementation.

Weight-Reducing Hennie Machines and Their Descriptional Complexity

Abstract: We present a constructive variant of the Hennie machine It is demonstrated how it can facilitate the design of finite-state machines We focus on the deterministic version of the model and study its descriptional complexity The model's succinctness is compared with common devices that include the nondeterministic finite automaton, two-way finite automaton and pebble automaton

Automata with Reversal-Bounded Counters: A Survey

Abstract: We survey the properties of automata augmented with reversal-bounded counters. In particular, we discuss the closure/non-closure properties of the languages accepted by these machines as well as the decidability/undecidability of decision problems concerning these devices. We also give applications to several problems in automata theory and formal languages.

Infinite-state energy games

Abstract: Energy games are a well-studied class of 2-player turn-based games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the cumulative changes non-negative in every component while the other tries to frustrate this. We consider generalized energy games played on infinite game graphs induced by pushdown automata (modelling recursion) or their subclass of one-counter automata. Our main result is that energy games are decidable in the case where the game graph is induced by a one-counter automaton and the energy is one-dimensional. On the other hand, every further generalization is undecidable: Energy games on one-counter automata with a 2-dimensional energy are undecidable, and energy games on pushdown automata are undecidable even if the energy is one-dimensional. Furthermore, we show that energy games and simulation games are inter-reducible, and thus we additionally obtain several new (un)decidability results for the problem of checking simulation preorder between pushdown automata and vector addition systems.

Word-Mappings of Level 2

Abstract: A sequence of natural numbers is said to have level k, for some natural integer k, if it can be computed by a deterministic pushdown automaton of level k (Fratani and Senizergues in Ann Pure Appl. Log. 141:363–411, 2006). We show here that the sequences of level 2 are exactly the rational formal power series over one undeterminate. More generally, we study mappings from words to words and show that the following classes coincide: the mappings which are computable by deterministic pushdown automata of level 2 the mappings which are solution of a system of catenative recurrence equations the mappings which are definable as a Lindenmayer system of type HDT0L. We illustrate the usefulness of this characterization by proving three statements about formal power series, rational sets of homomorphisms and equations in words.

Krivine machines and higher-order schemes

Abstract: We propose a new approach to analyzing higher-order recursive schemes. Many results in the literature use automata models generalizing pushdown automata, most notably higher-order pushdown automata with collapse (CPDA). Instead, we propose to use the Krivine machine model. Compared to CPDA, this model is closer to lambda-calculus, and incorporates nicely many invariants of computations, as for example the typing information. The usefulness of the proposed approach is demonstrated with new proofs of two central results in the field: the decidability of the local and global model checking problems for higher-order schemes with respect to the mu-calculus.

How Many Ants Does It Take to Find the Food

Abstract: Consider the Ants Nearby Treasure Search (ANTS) problem, where n mobile agents, initially placed at the origin of an infinite grid, collaboratively search for an adversarially hidden treasure. The agents are controlled by deterministic/randomized finite or pushdown automata and are able to communicate with each other through constant-size messages. We show that the minimum number of agents required to solve the ANTS problem crucially depends on the computational capabilities of the agents as well as the timing parameters of the execution environment. We give lower and upper bounds for different scenarios.

A Unifying Approach for Multistack Pushdown Automata

Abstract: We give a general approach to show the closure under complement and decide the emptiness for many classes of multistack visibly pushdown automata (Mvpa). A central notion in our approach is the visibly path-tree, i.e., a stack tree with the encoding of a path that denotes a linear ordering of the nodes. We show that the set of all such trees with a bounded size labeling is regular, and path-trees allow us to design simple conversions between tree automata and Mvpa’s. As corollaries of our results we get the closure under complement of ordered Mvpa that was an open problem, and a better upper bound on the algorithm to check the emptiness of bounded-phase Mvpa’s.

Infinite-State Energy Games

Abstract: Energy games are a well-studied class of 2-player turn-based games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the cumulative changes non-negative in every component while the other tries to frustrate this. We consider generalized energy games played on infinite game graphs induced by pushdown automata (modelling recursion) or their subclass of one-counter automata. Our main result is that energy games are decidable in the case where the game graph is induced by a one-counter automaton and the energy is one-dimensional. On the other hand, every further generalization is undecidable: Energy games on one-counter automata with a 2-dimensional energy are undecidable, and energy games on pushdown automata are undecidable even if the energy is one-dimensional. Furthermore, we show that energy games and simulation games are inter-reducible, and thus we additionally obtain several new (un)decidability results for the problem of checking simulation preorder between pushdown automata and vector addition systems.

The chomsky-schützenberger theorem for quantitative context-free languages

Abstract: Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative context-free languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schutzenberger Theorem for such quantitative context-free languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative context-free languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings. We also investigate under which conditions quantitative context-free languages assume only finitely many values.

Removing nondeterminism in constant height pushdown automata

Abstract: We study the descriptional cost of removing nondeterminism in constant height pushdown automata-i.e., pushdown automata with a built-in constant limit on the height of the pushdown. We show a double-exponential size increase when converting a constant height nondeterministic pushdown automaton into an equivalent deterministic device. Moreover, we prove that such a double-exponential blow-up cannot be avoided by certifying its optimality. As a direct consequence, we get that eliminating nondeterminism in classical finite state automata is single-exponential even with the help of a constant height pushdown store.

Language equivalence of probabilistic pushdown automata

Abstract: We study the language equivalence problem for probabilistic pushdown automata (pPDA) and their subclasses. We show that the problem is interreducible with the multiplicity equivalence problem for context-free grammars, the decidability of which has been open for several decades. Interreducibility also holds for pPDA with one control state. In contrast, for the case of a one-letter input alphabet we show that pPDA language equivalence (and hence multiplicity equivalence of context-free grammars) is in PSPACE and at least as hard as the polynomial identity testing problem.

Oracle Pushdown Automata, Nondeterministic Reducibilities, and the Hierarchy over the Family of Context-Free Languages

Abstract: We implement various oracle mechanisms on nondeterministic pushdown automata, which naturally induce nondeterministic reducibilities among formal languages in a theory of context-free languages. In particular, we examine a notion of nondeterministic many-one CFL-reducibility and carry out ground work of formulating a coherent framework for further expositions. Another more powerful reducibility—Turing CFL-reducibility—is also discussed in comparison. The Turing CFL-reducibility, in particular, makes it possible to induce a useful hierarchy (the CFL hierarchy) built over the family CFL of context-free languages. For each level of this hierarchy, basic structural properties are proven and three alternative characterizations are presented. We also show that the CFL hierarchy enjoys an upward collapse property. The first and second levels of the hierarchy are proven to be different. We argue that the CFL hierarchy coincides with a hierarchy over CFL built by applications of many-one CFL-reductions. Our goal is to provide a solid foundation for structural-complexity analyses in automata theory.

Fast Synchronization of Random Automata

Abstract: A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state deterministic automaton has a synchronizing word, then it has a synchronizing word of size at most (n-1)^2. Berlinkov recently made a breakthrough in the probabilistic analysis of synchronization by proving that with high probability, an automaton has a synchronizing word. In this article, we prove that with high probability an automaton admits a synchronizing word of length smaller than n^(1+\epsilon), and therefore that the Cerny conjecture holds with high probability.

LogCEP - Complex Event Processing based on Pushdown Automaton

Abstract: Complex (or Composite) event processing systems have become more popular in a number of areas. Non-deterministic finite automata (NFA) are frequently used to evaluate CEP queries. However, it is complex or difficult to use the traditional NFA-based method to process patterns with conjunction and negation. In this paper, we proposed a new CEP system LogCEP using pushdown automaton to support efficient processing of conjunction and negation. First, the semantic and query language specification of LogCEP system are presented. Then, an automaton named LogPDA is proposed for query processing in LogCEP system. LogPDA construction method describes how to convert a query to LogPDA automation. The LogPDA execution approach describes how to detect the specified pattern using LogPDA. Meanwhile, most of previous NFA-based optimizations can be employed to improve the evaluation efficiency. Finally, our simulation based experimental results show that our method not only extended the expressibility and processing capability but also didn't lead to efficiency decreasing.

Extended Two-Way Ordered Restarting Automata for Picture Languages

Abstract: We introduce a two-dimensional variant of the deterministic restarting automaton for processing rectangular pictures. Our device has a window of size three-by-three, in a rewrite step it can only replace the symbol in the central position of its window by a symbol that is smaller with respect to a fixed ordering on the tape alphabet, and it can only perform extended move-right and move-down steps. This automaton is strictly more expressive than the deterministic Sgraffito automaton, but its word problem can still be solved in polynomial time, and when restricted to one-dimensional input, it only accepts the regular languages.

Teaching push-down automata and Turing machines

Abstract: In this paper we present the new version of a tool to assist in teaching formal languages and automata theory. In the previous version the tool provided algorithms for regular expressions, finite automata and context free grammars. The new version can simulate as well push-down automata and Turing machines.

Verifying probabilistic systems : new algorithms and complexity results

Abstract: The content of the dissertation falls in the area of formal verification of probabilistic systems. It comprises four parts listed below: 1. the decision problem of (probabilistic) simulation preorder between probabilistic pushdown automata (pPDAs) and finite probabilistic automata (fPAs); 2. the decision problem of a bisimilarity metric on finite probabilistic automata (fPAs); 3. the approximation problem of acceptance probability of deterministictimed-automata (DTA) objectives on continuous-time Markov chains (CTMCs); 4. the approximation problem of cost-bounded reachability probability on continuous-time Markov decision processes (CTMDPs). The first two parts are concerned with equivalence checking on probabilistic automata, where probabilistic automata (PAs) are an analogue of discretetime Markov decision processes that involves both non-determinism and discrete-time stochastic transitions. The last two parts are concerned with numerical algorithms on Markov jump processes. In Part 1 and Part 2, we mainly focus on complexity issues; as for Part 3 and Part 4, we mainly focus on numerical approximation algorithms. In Part 1, we prove that the decision problem of (probabilistic) simulation preorder between pPDAs and fPAs is in EXPTIME. A pPDA is a pushdown automaton extended with probabilistic transitions, and generally it induces an infinite-state PA. The simulation preorder is a preorder that characterizes whether one probabilistic process (modelled as a PA) can mimic the other; technically speaking, it is the one-sided version of (probabilistic) bisimulation, which instead characterizes whether two probabilistic processes are behaviourally equivalent. We demonstrate the EXPTIME-membership of the decision problem through a tableaux system and a partition-refinement algorithm. Combined with the EXPTIMEhardness result by Kucera and Mayr (2010), we are able to show that the decision problem is EXPTIME-complete. The complexity result coincides with the one by Kucera and Mayr (2010) on non-probabilistic pushdown automata. Moreover, we obtain a fixed-parameter-tractable result on this