Showing papers on "Deterministic pushdown automaton published in 2016"

Limit-Deterministic Büchi Automata for Linear Temporal Logic

Abstract: Limit-deterministic Buchi automata can replace deterministic Rabin automata in probabilistic model checking algorithms, and can be significantly smaller. We present a direct construction from an LTL formula \(\varphi \) to a limit-deterministic Buchi automaton. The automaton is the combination of a non-deterministic component, guessing the set of eventually true \({\mathbf {G}}\)-subformulas of \(\varphi \), and a deterministic component verifying this guess and using this information to decide on acceptance. Contrary to the indirect approach of constructing a non-deterministic automaton for \(\varphi \) and then applying a semi-determinisation algorithm, our translation is compositional and has a clear logical structure. Moreover, due to its special structure, the resulting automaton can be used not only for qualitative, but also for quantitative verification of MDPs, using the same model checking algorithm as for deterministic automata. This allows one to reuse existing efficient implementations of this algorithm without any modification. Our construction yields much smaller automata for formulas with deep nesting of modal operators and performs at least as well as the existing approaches on general formulas.

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 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 some interesting consequences, such as, the closure under complement, the decidability of universality, inclusion and equality, and the effective semilinearity of the Parikh image (Parikh's theorem). As a further contribution, we give a logical characterization and compare the expressiveness of the scope-bounded restriction with other MVPA classes from the literature. To the best of our knowledge, scoped MVPA languages form the largest class of formal languages accepted by MPA that enjoys all the above nice properties.

A Logical Characterization for Dense-Time Visibly Pushdown Automata

Abstract: Two of the most celebrated results that effectively exploit visual representation to give logical characterization and decidable model-checking include visibly pushdown automata (VPA) by Alur and Madhusudan and event-clock automata (ECA) by Alur, Fix and Henzinger. VPA and ECA—by making the call-return edges visible and by making the clock-reset operation visible, respectively—recover decidability for the verification problem for pushdown automata implementation against visibly pushdown automata specification and timed automata implementation against event-clock timed automata specification, respectively. In this work we combine and extend these two works to introduce dense-time visibly pushdown automata that make both the call-return as well as resets visible. We present MSO logic characterization of these automata and prove the decidability of the emptiness problem for these automata paving way for verification problem for dense-timed pushdown automata against dense-timed visibly pushdown automata specification.

Fuzzy state grammar and fuzzy deep pushdown automaton

Abstract: Motivated by the concept of fuzzy finite automata and fuzzy pushdown automata, we investigate a novel fuzzy state grammars and fuzzy deep pushdown automata concept. This concept represents a natural extension of contemporary state grammar and deep pushdown automaton, making them more robust in terms of imprecision, errors, and uncertainty. It has been proved that we can construct fuzzy deep pushdown automata from fuzzy state grammars and vice-versa. Furthermore, it has been proved that if fuzzy deep pushdown automaton Mfd is constructed from fuzzy state grammar Gfs then L(Mfd) = L(Gfs). In other words, for any string α ∈ � ∗ , μ(α; α ∈ L(Gfs)) = μ(α; α ∈ L(Mfd)) where μ denotes the membership of a string.

Invisible Pushdown Languages

Abstract: Context-free languages allow one to express data with hierarchical structure, at the cost of losing some of the useful properties of languages recognized by finite automata on words. However, it is possible to restore some of these properties by making the structure of the tree visible, such as is done by visibly pushdown languages, or finite automata on trees. In this paper, we show that the structure given by such approaches remains invisible when it is read by a finite automaton (on word). In particular, we show that separability with a regular language is undecidable for visibly pushdown languages, just as it is undecidable for general context-free languages.

On the Effects of Nondeterminism on Ordered Restarting Automata

Abstract: While stateless deterministic ordered restarting automata accept exactly the regular languages, it is known that nondeterministic ordered restarting automata accept some languages that are not context-free. Here we show that, in fact, the class of languages accepted by these automata is an abstract family of languages that is incomparable to the linear languages, the context-free languages, and the growing context-sensitive languages with respect to inclusion, and that the emptiness problem is decidable for these languages. In addition, it is shown that stateless ordered restarting automata just accept regular languages, and we present an infinite family of regular languages $$C_n$$ such that $$C_n$$ is accepted by a stateless ordered restarting automaton with an alphabet of size On, but each stateless deterministic ordered restarting automaton for $$C_n$$ needs $$2^{On}$$ letters.

Families of DFAs as Acceptors of $\omega$-Regular Languages

Abstract: Families of DFAs (FDFAs) provide an alternative formalism for recognizing $\omega$-regular languages The motivation for introducing them was a desired correlation between the automaton states and right congruence relations, in a manner similar to the Myhill-Nerode theorem for regular languages This correlation is beneficial for learning algorithms, and indeed it was recently shown that $\omega$-regular languages can be learned from membership and equivalence queries, using FDFAs as the acceptors In this paper, we look into the question of how suitable FDFAs are for defining omega-regular languages Specifically, we look into the complexity of performing Boolean operations, such as complementation and intersection, on FDFAs, the complexity of solving decision problems, such as emptiness and language containment, and the succinctness of FDFAs compared to standard deterministic and nondeterministic $\omega$-automata We show that FDFAs enjoy the benefits of deterministic automata with respect to Boolean operations and decision problems Namely, they can all be performed in nondeterministic logarithmic space We provide polynomial translations of deterministic B\"uchi and co-B\"uchi automata to FDFAs and of FDFAs to nondeterministic B\"uchi automata (NBAs) We show that translation of an NBA to an FDFA may involve an exponential blowup Last, we show that FDFAs are more succinct than deterministic parity automata (DPAs) in the sense that translating a DPA to an FDFA can always be done with only a polynomial increase, yet the other direction involves an inevitable exponential blowup in the worst case

New Results on the Minimum Amount of Useful Space

Abstract: We present several new results on minimal space requirements to recognize a nonregular language: (i) realtime nondeterministic Turing machines can recognize a nonregular unary language within weak log log n space, (ii) log log n is a tight space lower bound for accepting general nonregular languages on weak realtime pushdown automata, (iii) there exist unary nonregular languages accepted by realtime alternating one-counter automata within weak log n space, (iv) there exist nonregular languages accepted by two-way deterministic pushdown automata within strong log log n space, and, (v) there exist unary nonregular languages accepted by two-way one-counter automata using quantum and classical states with middle log n space and bounded error.

A Perfect Class of Context-Sensitive Timed Languages

Abstract: Perfect languages--a term coined by Esparza, Ganty, and Majumdar--are the classes of languages that are closed under Boolean operations and enjoy decidable emptiness problem. Perfect languages form the basis for decidable automata-theoretic model-checking for the respective class of models. Regular languages and visibly pushdown languages are paradigmatic examples of perfect languages. Alur and Dill initiated the language-theoretic study of timed languages and introduced timed automata capturing a timed analog of regular languages. However, unlike their untimed counterparts, timed regular languages are not perfect. Alur, Fix, and Henzinger later discovered a perfect subclass of timed languages recognized by event-clock automata. Since then, a number of perfect subclasses of timed context-free languages, such as event-clock visibly pushdown languages, have been proposed. There exist examples of perfect languages even beyond context-free languages:--La Torre, Madhusudan, and Parlato characterized first perfect class of context-sensitive languages via multistack visibly pushdown automata with an explicit bound on number of stages where in each stage at most one stack is used. In this paper we extend their work for timed languages by characterizing a perfect subclass of timed context-sensitive languages called dense-time multistack visibly pushdown languages and provide a logical characterization for this class of timed languages.

The Hoare Logic of Deterministic and Nondeterministic Monadic Recursion Schemes

Abstract: The equational theory of deterministic monadic recursion schemes is known to be decidable by the result of Senizergues on the decidability of the problem of DPDA equivalence. In order to capture some properties of the domain of computation, we augment equations with certain hypotheses. This preserves the decidability of the theory, which we call simple implicational theory. The asymptotically fastest algorithm known for deciding the equational theory, and also for deciding the simple implicational theory, has a running time that is nonelementary. We therefore consider a restriction of the properties about schemes to check: instead of arbitrary equations f ≡ g between schemes, we focus on propositional Hoare assertions lprflqr, where f is a scheme and p, q are tests. Such Hoare assertions have a straightforward encoding as equations. For this subclass of program properties, we can also handle nondeterminism at the syntactic and/or at the semantic level, without increasing the complexity of the theories. We investigate the Hoare theory of monadic recursion schemes, that is, the set of valid implications whose conclusions are Hoare assertions and whose premises are of a certain simple form. We present a sound and complete Hoare-style calculus for this theory. We also show that the Hoare theory can be decided in exponential time, and that it is complete for this class.

Supervisory control synthesis for deterministic context free specification languages

Abstract: This paper describes two steps in the generalization of supervisory control theory to situations where the specification is modeled by a deterministic context free language (DCFL). First, it summarizes a conceptual iterative algorithm from Schneider et al. (2014) solving the supervisory control problem for language models. This algorithm involves two basic iterative functions. Second, the main part of this paper presents an implementable algorithm realizing one of these functions, namely the calculation of the largest controllable marked sublanguage of a given DCFL. This algorithm least restrictively removes controllability problems in a deterministic pushdown automaton realizing this DCFL.

Two-Way Visibly Pushdown Automata and Transducers

Abstract: Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three following models are equivalent: deterministic two-way transducers, monadic second-order (MSO) transducers, and deterministic one-way automata equipped with a finite number of registers. Nested words are words with a nesting structure, allowing to model unranked trees as their depth-first-search linearisations. In this paper, we consider transformations from nested words to words, allowing in particular to produce unranked trees if output words have a nesting structure. The model of visibly pushdown transducers allows to describe such transformations, and we propose a simple deterministic extension of this model with two-way moves that has the following properties: i) it is a simple computational model, that naturally has a good evaluation complexity; ii) it is expressive: it subsumes nested word-to-word MSO transducers, and the exact expressiveness of MSO transducers is recovered using a simple syntactic restriction; iii) it has good algorithmic/closure properties: the model is closed under composition with a unambiguous one-way letter-to-letter transducer which gives closure under regular look-around, and has a decidable equivalence problem.

A Practical Simulation Result for Two-Way Pushdown Automata

Abstract: The simulation of two-way deterministic and nondeterministic pushdown automata is revisited. A uniform algorithm presented herein decides on a random-access machine in linear time resp. cubic time whether a given pushdown automaton accepts a word, while the actual run of the automaton may take exponential time. The algorithm is practical since it only explores reachable configurations, simulates a class of quasi-deterministic decision problems in linear time even if the pushdown automaton is nondeterministic, and iterates over a simple work list. This is an improvement over previous simulation algorithms.

Prediction of Infinite Words with Automata

Abstract: In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the predictor's guesses are correct. In this paper we consider the case in which the predictor is an automaton and the emitted values are drawn from a finite set; i.e., the emitted sequence is an infinite word. We examine the predictive capabilities of finite automata, pushdown automata, stack automata a generalization of pushdown automata, and multihead finite automata. We relate our predicting automata to purely periodic words, ultimately periodic words, and multilinear words, describing novel prediction algorithms for mastering these sequences.

When input-driven pushdown automata meet reversiblity

Abstract: We investigate subfamilies of context-free languages that share two important properties. The languages are accepted by input-driven pushdown automata as well as by a reversible pushdown automata. So, the languages are input driven and reversible at the same time. This intersection can be defined on the underlying language families or on the underlying machine classes. It turns out that the latter class is properly included in the former. The relationships between the language families obtained in this way and to reversible context-free languages as well as to input-driven languages are studied. In general, a hierarchical inclusion structure within the real-time deterministic context-free languages is obtained. Finally, the closure properties of these families under the standard operations are investigated and it turns out that all language families introduced are anti-AFLs.

Some Subclasses of Linear Languages based on Nondeterministic Linear Automata

Abstract: In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this paper is to introduce the deterministic linear automata and even linear automata, i.e. the natural restriction of nondeterministic linear automata for the deterministic and even linear language classes, respectively. In particular, there are different, but not equivalents, proposals for the class of "deterministic" linear languages. We proved here that the class of languages accepted by the deterministic linear automata are not contained in any of the these classes and in fact they properly contain these classes. Another, contribution is the generation of an infinite hierarchy of formal languages, going from the class of languages accepted by deterministic linear automata and achieved, in the limit, the class of linear languages.

Visibly Pushdown Transducers with Well-Nested Outputs

Abstract: Visibly pushdown transducers (VPTs) are visibly pushdown automata extended with outputs. They have been introduced oto model transformations of nested words, i.e. words with a call/return structure. When outputs are also structured and well nested words, VPTs are a natural formalism to express tree transformations evaluated in streaming. We prove the class of VPTs with well-nested outputs to be decidable in PTIME. Moreover, we show that this class is closed under composition and that its type-checking against visibly pushdown languages is decidable.

On Ordered RRWW-Automata

Abstract: It is known that the deterministic ordered restarting automaton accepts exactly the regular languages, while its nondeterministic variant accepts some languages that are not even growing context-sensitive. Here we study an extension of the ordered restarting automaton, the so-called ORRWW-automaton, which is obtained from the previous model by separating the restart operation from the rewrite operation. First we show that the deterministic ORRWW-automaton still characterizes just the regular languages. Then we prove that this also holds for the stateless variant of the nondeterministic ORRWW-automaton, which is obtained by splitting the transition relation into two parts, where the first part is used until a rewrite operation is performed, and the second part is used thereafter. Finally, we show that the nondeterministic ORRWW-automaton is even more expressive than the nondeterministic ordered restarting automaton.

On minimal realization of if-languages: a categorical approach

Abstract: The purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton pre- sented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deter- ministic automata with IF-outputs and IF-languages alongwith a functorial relationship between them are introduced

On a Class of Automaton Algebras

Abstract: Abstract We show that every finitely generated algebra that is a finitely generated module over a finitely generated commutative subalgebra is an automaton algebra in the sense of Ufnarovskii.

On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited

Abstract: We consider the complexity of integer base expansions of algebraic irrational numbers from a computational point of view. We show that the Hartmanis--Stearns problem can be solved in a satisfactory way for the class of multistack machines. In this direction, our main result is that the base-$b$ expansion of an algebraic irrational real number cannot be generated by a deterministic pushdown automaton. We also confirm an old claim of Cobham proving that such numbers cannot be generated by a tag machine with dilation factor larger than one.

Bounded-oscillation Pushdown Automata

Abstract: We present an underapproximation for context-free languages by filtering out runs of the underlying pushdown automaton depending on how the stack height evolves over time. In particular, we assign to each run a number quantifying the oscillating behavior of the stack along the run. We study languages accepted by pushdown automata restricted to k-oscillating runs. We relate oscillation on pushdown automata with a counterpart restriction on context-free grammars. We also provide a way to filter all but the k-oscillating runs from a given PDA by annotating stack symbols with information about the oscillation. Finally, we study closure properties of the defined class of languages and the complexity of the k-emptiness problem asking, given a pushdown automaton P and k >= 0, whether P has a k-oscillating run. We show that, when k is not part of the input, the k-emptiness problem is NLOGSPACE-complete.

From μ-Regular Expressions to Pushdown Automata.

Abstract: We extend Antimirov's partial derivatives from regular expressions to $\mu$-regular expressions that describe context-free languages. We prove the correctness of partial derivatives as well as the finiteness of the set of iterated partial derivatives. The latter are used as pushdown symbols in our construction of a nondeterministic pushdown automaton, which generalizes Antimirov's NFA construction.