Showing papers on "ω-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.

Markov Chains and Unambiguous Büchi Automata

Abstract: Unambiguous automata, i.e., nondeterministic automata with the restriction of having at most one accepting run over a word, have the potential to be used instead of deterministic automata in settings where nondeterministic automata can not be applied in general. In this paper, we provide a polynomially time-bounded algorithm for probabilistic model checking of discrete-time Markov chains against unambiguous Buchi automata specifications and report on our implementation and experiments.

Complementing Semi-deterministic Büchi Automata

Abstract: We introduce an efficient complementation technique for semi-deterministic Buchi automata, which are Buchi automata that are deterministic in the limit: from every accepting state onward, their behaviour is deterministic. It is interesting to study semi-deterministic automata, because they play a role in practical applications of automata theory, such as the analysis of Markov decision processes. Our motivation to study their complementation comes from the termination analysis implemented in Ultimate Buchi Automizer, where these automata represent checked runs and have to be complemented to identify runs to be checked. We show that semi-determinism leads to a simpler complementation procedure: an extended breakpoint construction that allows for symbolic implementation. It also leads to significantly improved bounds as the complement of a semi-deterministic automaton with n states has less than $$4^n$$ states. Moreover, the resulting automaton is unambiguous, which again offers new applications, like the analysis of Markov chains. We have evaluated our construction against the semi-deterministic automata produced by the Ultimate Buchi Automizer. The evaluation confirms that our algorithm outperforms the known complementation techniques for general nondeterministic Buchi automata.

From LTL to deterministic automata

Abstract: We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula $$\varphi $$ź. The automaton is the product of a co-Buchi automaton for $$\varphi $$ź and an array of Rabin automata, one for each $${\mathbf {G}}$$G-subformula of $$\varphi $$ź. The Rabin automaton for $${\mathbf {G}}\psi $$Gź is in charge of recognizing whether $${\mathbf {F}}{\mathbf {G}}\psi $$FGź holds. This information is passed to the co-Buchi automaton that decides on acceptance. As opposed to standard procedures based on Safra's determinization, the states of all our automata have a clear logical structure, which allows for various optimizations. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.

Dynamic input/output automata

Abstract: We present dynamic I/O automata (DIOA), a compositional model of dynamic systems. In DIOA, automata can be created and destroyed dynamically, as computation proceeds, and an automaton can dynamically change its signature, i.e., the set of actions in which it can participate.DIOA features operators for parallel composition, action hiding, action renaming, a notion of automaton creation, and a notion of behavioral subtyping by means of trace inclusion. DIOA can model mobility, using signature modification, and is hierarchical: a dynamically changing system of interacting automata is itself modeled as a single automaton.We also show that parallel composition, action hiding, action renaming, and (subject to some technical conditions) automaton creation are all monotonic with respect to trace inclusion: if one component is replaced by another whose traces are a subset of the former, then the set of traces of the system as a whole can only be reduced.

One-Way Jumping Finite Automata

Abstract: We propose the one-way jumping finite automaton model, restricting the jumping relation of the recently introduced jumping finite automaton so that the machine can only jump over symbols it cannot process in its current state. The reading head of a one-way jumping finite automaton moves deterministically in one direction within the input word, whereas movement of the reading head of jumping finite automaton is non-deterministic. The class of languages accepted by one-way jumping finite automata is different from that of jumping finite automata, in particular, it includes all regular languages, as opposed to the latter. We study one-way jumping finite automata and obtain closure properties, a pumping lemma, and separation results with respect to the classical language classes of the Chomsky hierarchy.

Completely Reachable Automata

Abstract: We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.

Problems on Finite Automata and the Exponential Time Hypothesis

Abstract: We study several classical decision problems on finite automata under the (Strong) Exponential Time Hypothesis. We focus on three types of problems: universality, equivalence, and emptiness of intersection. All these problems are known to be CoNP-hard for nondeterministic finite automata, even when restricted to unary input alphabets. A different type of problems on finite automata relates to aperiodicity and to synchronizing words. We also consider finite automata that work on commutative alphabets and those working on two-dimensional words.

Goal-Oriented Reduction of Automata Networks

Abstract: We consider networks of finite-state machines having local transitions conditioned by the current state of other automata. In this paper, we introduce a reduction procedure tailored for reachability properties of the form “from global state \({s}\), there exists a sequence of transitions leading to a state where an automaton g is in a local state \(\top \)”. By analysing the causality of transitions within the individual automata, the reduction identifies local transitions which can be removed while preserving all the minimal traces satisfying the reachability property. The complexity of the procedure is polynomial with the total number of local transitions, and exponential with the maximal number of local states within an automaton. Applied to Boolean and multi-valued networks modelling dynamics of biological systems, the reduction can shrink down significantly the reachable state space, enhancing the tractability of the model-checking of large networks.

Execution information rate for some classes of automata

Abstract: We study the Shannon information rate of accepting runs of various forms of automata. This rate is a complexity indicator for executions of these automata. Accepting runs of finite automata and reversal-bounded nondeterministic counter machines, as well as their restrictions and variations, are investigated and are shown, in many cases, to have computable execution rates. We also study the information rate of behaviors in discrete timed automata. We conduct experiments on C programs showing that estimating the information rates for their executions is feasible in many cases.

Reduction of Nondeterministic Tree Automata

Abstract: We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It uses criteria based on combinations of downward and upward simulation preorder on trees, and the more general downward and upward language inclusions. Since tree-language inclusion is EXPTIME-complete, we describe methods to compute good approximations in polynomial time. We implemented our algorithm as a module of the well-known libvata tree automata library, and tested its performance on a given collection of tree automata from various applications of libvata in regular model checking and shape analysis, as well as on various classes of randomly generated tree automata. Our algorithm yields substantially smaller and sparser automata than all previously known reduction techniques, and it is still fast enough to handle large instances.

Language Recognition Power and Succinctness of Affine Automata

Abstract: In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by Diaz-Caro and Yakaryilmaz [6] referred as affine automata. First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which allows us to characterize the class of exclusive stochastic languages. Then, we initiate a study on the succintness of affine automata. In particular, we show that an infinite family of unary regular languages can be recognized by 2-state affine automata, whereas the number of states of any quantum and probabilistic automata cannot be bounded. Finally, we present the characterization of all regular unary languages recognized by two-state affine automata.

Walking on Data Words

Abstract: Data words are words with additional edges that connect pairs of positions carrying the same data value. We consider a natural model of automaton walking on data words, called Data Walking Automaton, and study its closure properties, expressiveness, and the complexity of some basic decision problems. Specifically, we show that the class of deterministic Data Walking Automata is closed under all Boolean operations, and that the class of non-deterministic Data Walking Automata has decidable emptiness, universality, and containment problems. We also prove that deterministic Data Walking Automata are strictly less expressive than non-deterministic Data Walking Automata, which in turn are captured by Class Memory Automata.

On Finite and Polynomial Ambiguity of Weighted Tree Automata

Abstract: We consider finite and polynomial ambiguity of weighted tree automata. Concerning finite ambiguity, we show that a finitely ambiguous weighted tree automaton can be decomposed into a sum of unambiguous automata. For polynomial ambiguity, we show how to decompose a polynomially ambiguous weighted tree automaton into simpler polynomially ambiguous automata and then analyze the structure of these simpler automata. We also outline how these results can be used to capture the ambiguity of weighted tree automata with weighted logics.

A new distributed learning automata based algorithm for maximum independent set problem

Abstract: Maximum independent set problem is an NP-Hard one with the aim of finding the set of independent vertices with maximum possible cardinality in a graph. In this paper, we investigate a learning automaton based algorithm that finds a maximum independent set in the graph. Initially, a learning automaton is assigned to each vertex of graph. In order to find candidate independent set, a set of distributed learning automata collaborate with each other. The proposed algorithm based on learning automata is guided iteratively to the maximum independent set by updating the action probability vector. In order to study the performance of the proposed algorithm, we conducted some experiments. The reported numerical results confirm the superiority of our proposed algorithm in terms of cardinality of the obtained solution.

Two-way representations and weighted automata

Abstract: We study the series realized by weighted two-way automata, that are strictly more powerful than weighted one-way automata. To this end, we consider the Hadamard product and the Hadamard iteration of formal power series. We introduce two-way representations and show that the series they realize are the solutions of fixed-point equations. In rationally additive semirings, we prove that two-way automata are equivalent to two-way representations, and, for some specific classes of two-way automata, rotating and sweeping automata, we give a characterization of the series that can be realized.

Weighted Symbolic Automata with Data Storage

Abstract: We introduce weighted symbolic automata with data storage, which combine and generalize the concepts of automata with storage types, weighted automata, and symbolic automata. By defining two particular data storages, we show that this combination is rich enough to capture symbolic visibly pushdown automata and weighted timed automata. We introduce a weighted MSO-logic and prove a Buchi-Elgot-Trakhtenbrot theorem, i.e., the new logic and the new automaton model are expressively equivalent.

Quantum Finite Automata

Abstract: Various quantum versions o f the most basic models o f the classical finite automata have already been introduced and various modes of their computations have already started t o be investigated. In this paper we overview basic models, approaches, techniques and results in this promising area of quantum automata that is expected to play an important role also in theoretical computer science. We also summarize some open problems and research directions to pursue in this area.

Analyzing Timed Systems Using Tree Automata

Abstract: Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract properties, such as state reachability. We propose a new technique to analyze such timed systems using finite tree automata instead of finite word automata. The main idea is to consider timed behaviors as graphs with matching edges capturing timing constraints. When a family of graphs has bounded tree-width, they can be interpreted in trees and MSO-definable properties of such graphs can be checked using tree automata. The technique is quite general and applies to many timed systems. In this paper, as an example, we develop the technique on timed pushdown systems, which have recently received considerable attention. Further, we also demonstrate how we can use it on timed automata and timed multi-stack pushdown systems (with boundedness restrictions).

Nested Weighted Limit-Average Automata of Bounded Width

Abstract: While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness.

Automata theory and higher-order model-checking

Abstract: In verification, an automata theoretic approach is by now a standard. In order to extend this approach to higher-order programs we need a good understanding of higher-order control flow, and for this semantics has the right tools. We present some results and methods of this subject between automata theory and semantics.

Learning Deterministic Finite Automata from Infinite Alphabets

Abstract: We proposes an algorithm to learn automata infinite alphabets, or at least too large to enumerate. We apply it to define a generic model intended for regression, with transitions constrained by intervals over the alphabet. The algorithm is based on the Red & Blue framework for learning from an input sample. We show two small case studies where the alphabets are respectively the natural and real numbers, and show how nice properties of automata models like interpretability and graphical representation transfer to regression where typical models are hard to interpret.

The Bridge Between Regular Cost Functions and Omega-Regular Languages

Abstract: In this paper, we exhibit a one-to-one correspondence between omega-regular languages and a subclass of regular cost functions over finite words, called omega-regular like cost functions. This bridge between the two models allows one to readily import classical results such as the last appearance record or the McNaughton-Safra constructions to the realm of regular cost functions. In combination with game theoretic techniques, this also yields a simple description of an optimal procedure of history-determinisation for cost automata, a central result in the theory of regular cost functions.

An Automata Characterisation for Multiple Context-Free Languages

Abstract: We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.

The Garden of Eden Theorem for Cellular Automata on Group Sets

Abstract: We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an automaton is surjective if and only if it is pre-injective. Pre-Injectivity means that two global configurations that differ at most on a finite subset and have the same image under the global transition function must be identical.

Minimal and Reduced Reversible Automata

Abstract: A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration. It is also observed that there exist reduced reversible automata which are not minimal, in the sense that all the automata obtained by merging some of their equivalent states are irreversible. Furthermore, it is proved that if the minimum deterministic automaton accepting a reversible language contains a loop in the “irreversible part” then it is always possible to construct infinitely many reduced reversible automata accepting such a language.

Quantitative Automata under Probabilistic Semantics

Abstract: Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of quantitative functions, we establish that automata with monitor counters and nested weighted automata are equivalent. We study for the first time such quantitative automata under probabilistic semantics. We show that several problems that are undecidable for the classical questions of emptiness and universality become decidable under the probabilistic semantics. We present a complete picture of decidability for such automata, and even an almost-complete picture of computational complexity, for the probabilistic questions we consider.

Minimization of Symbolic Tree Automata

Abstract: Symbolic tree automata allow transitions to carry predicates over rich alphabet theories, such as linear arithmetic, and therefore extend finite tree automata to operate over infinite alphabets, such as the set of rational numbers. Existing tree automata algorithms rely on the alphabet being finite, and generalizing them to the symbolic setting is not a trivial task. In this paper we study the problem of minimizing symbolic tree automata. First, we formally define and prove the properties of minimality in the symbolic setting. Second, we lift existing minimization algorithms to symbolic tree automata. Third, we present a new algorithm based on the following idea: the problem of minimizing symbolic tree automata can be reduced to the problem of minimizing symbolic (string) automata by encoding the tree structure as part of the alphabet theory. We implement and evaluate all our algorithms against existing implementations and show that the symbolic algorithms scale to large alphabets and can minimize automata over complex alphabet theories.