Topic
Quantum finite automata
About: Quantum finite automata is a research topic. Over the lifetime, 3725 publications have been published within this topic receiving 96542 citations.
Papers published on a yearly basis
Papers
More filters
01 Jan 1993
TL;DR: It is proved that a polynomial-time learning algorithm for Boolean formulae, deterministic finite automata or constant-depth threshold circuits would have dramatic consequences for cryptography and number theory and is applied to obtain strong intractability results for approximating a generalization of graph coloring.
Abstract: In this paper, we prove the intractability of learning several classes of Boolean functions in the distribution-free model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are representation independent, in that they hold regardless of the syntactic form in which the learner chooses to represent its hypotheses.Our methods reduce the problems of cracking a number of well-known public-key cryptosystems to the learning problems. We prove that a polynomial-time learning algorithm for Boolean formulae, deterministic finite automata or constant-depth threshold circuits would have dramatic consequences for cryptography and number theory. In particular, such an algorithm could be used to break the RSA cryptosystem, factor Blum integers (composite numbers equivalent to 3 modulo 4), and detect quadratic residues. The results hold even if the learning algorithm is only required to obtain a slight advantage in prediction over random guessing. The techniques used demonstrate an interesting duality between learning and cryptography.We also apply our results to obtain strong intractability results for approximating a generalization of graph coloring.
504 citations
Book•
01 Jan 1986
TL;DR: This chapter discusses models for Finite Automata Regular Expressions Context-Free Grammars Pushdown Automata Turing Machines Functions, Relations, and Translations, and properties of these models.
Abstract: Part 1 Introduction: Preliminaries Languages and Computation. Part 2 Models: Finite Automata Regular Expressions Context-Free Grammars Pushdown Automata Turing Machines Functions, Relations, and Translations. Part 3 Properties: Family Relationships Closure Properties Decision Problems. Part 4 Onward: Further Topics.
502 citations
TL;DR: Is Nature, Underneath It All, a CA?
Abstract: * Introduction: Preliminary Musings * Formalism * Phenomenological Studies of Generic CA * Dynamical Systems Theory Approach * Analytic Approach * Cellular Automata and Language Theory * Probabilistic CA * Generalized Models * CA Models of Fluid Dynamics * Neural Networks * Artificial-Life * Is Nature, Underneath It All, a CA?
488 citations
TL;DR: A largely phenomenological study of two-dimensional cellular automata is reported, finding Qualitative classes of behavior similar to those in one-dimensional Cellular automata are found.
Abstract: A largely phenomenological study of two-dimensional cellular automata is reported. Qualitative classes of behavior similar to those in one-dimensional cellular automata are found. Growth from simple seeds in two-dimensiona! cellular automata can produce patterns with complicated boundaries, characterized by a variety of growth dimensions. Evolution from disordered states can give domains with boundaries that execute effectively continuous motions. Some global properties of cellular automata can be described by entropies and Lyapunov exponents. Others are undecidable.
467 citations
TL;DR: Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata, and the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities.
Abstract: Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations.
429 citations