Continuous automaton

About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.

Learning the Language of Error

Abstract: We propose to harness Angluin’s \(L^*\) algorithm for learning a deterministic finite automaton that describes the possible scenarios under which a given program error occurs. The alphabet of this automaton is given by the user (for instance, a subset of the function call sites or branches), and hence the automaton describes a user-defined abstraction of those scenarios. More generally, the same technique can be used for visualising the behavior of a program or parts thereof. This can be used, for example, for visually comparing different versions of a program, by presenting an automaton for the behavior in the symmetric difference between them, or for assisting in merging several development branches. We present initial experiments that demonstrate the power of an abstract visual representation of errors and of program segments.

The finiteness problem for automaton semigroups is undecidable

Abstract: The finiteness problem for automaton groups and semigroups has been widely studied, several partial positive results are known. However we prove that, in the most general case, the problem is undecidable. We study the case of automaton semigroups. Given a NW-deterministic Wang tile set, we construct an Mealy automaton, such that the plane admit a valid Wang tiling if and only if the Mealy automaton generates a finite semigroup. The construction is similar to a construction by Kari for proving that the nilpotency problem for cellular automata is unsolvable. Moreover Kari proves that the tiling of the plane is undecidable for NW-deterministic Wang tile set. It follows that the finiteness problem for automaton semigroup is undecidable.

Algorithms for guided tree automata

Abstract: When reading an input tree, a bottom-up tree automaton is unaware of where it is relative to the root. This problem is important to the efficient implementation of decision procedures for the Monadic Second-order Logic (M2L) on finite trees. In [KS97], it is shown how exponential state space blow-ups may occur in common situations. The analysis of the problem leads to the notion of guided tree automaton for combatting such explosions. The guided automaton is equipped with separate state spaces that are assigned by a top-down automaton, called the guide. In this paper, we explore the algorithmic and practical problems arising from this relatively complicated automaton concept. Our solutions are based on a BDD representation of automata [HJJ + 96], which allows the practical handling of automata on very large alphabets. In addition, we propose data structures for avoiding the quadratic size of transition tables associated with tree automata. We formulate and analyze product, projection (subset construction), and minimization algorithms for guided tree automata. We show that our product algorithm for certain languages are asymptotically faster than the usual algorithm that relies on transition tables. Also, we provide some preliminary experimental results on the use of guided automata vs. standard tree automata.

Truly on-the-fly LTL model checking

Abstract: We propose a novel algorithm for automata-based LTL model checking that interleaves the construction of the generalized Buchi automaton for the negation of the formula and the emptiness check. Our algorithm first converts the LTL formula into a linear weak alternating automaton; configurations of the alternating automaton correspond to the locations of a generalized Buchi automaton, and a variant of Tarjan's algorithm is used to decide the existence of an accepting run of the product of the transition system and the automaton. Because we avoid an explicit construction of the Buchi automaton, our approach can yield significant improvements in runtime and memory, for large LTL formulas. The algorithm has been implemented within the Spin model checker, and we present experimental results for some benchmark examples.

Symbolic computation using cellular automata-based hyperdimensional computing

Abstract: This letter introduces a novel framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation. A 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 shown to be capable of long-term memory, and it requires orders of magnitude less computation compared to echo state networks. As the focus of the letter, we suggest that binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing. To demonstrate the capability of the proposed system, we make analogies directly on image data by asking, What is the automobile of air?