15,842 research outputs found

    On two-way communication in cellular automata with a fixed number of cells

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    The effect of adding two-way communication to k cells one-way cellular automata (kC-OCAs) on their size of description is studied. kC-OCAs are a parallel model for the regular languages that consists of an array of k identical deterministic finite automata (DFAs), called cells, operating in parallel. Each cell gets information from its right neighbor only. In this paper, two models with different amounts of two-way communication are investigated. Both models always achieve quadratic savings when compared to DFAs. When compared to a one-way cellular model, the result is that minimum two-way communication can achieve at most quadratic savings whereas maximum two-way communication may provide savings bounded by a polynomial of degree k

    Synchronizing Automata on Quasi Eulerian Digraph

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    In 1964 \v{C}ern\'{y} conjectured that each nn-state synchronizing automaton posesses a reset word of length at most (n1)2(n-1)^2. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in nn. Thus the main problem here is to prove quadratic (in nn) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

    Emptiness of Zero Automata Is Decidable

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    Zero automata are a probabilistic extension of parity automata on infinite trees. The satisfiability of a certain probabilistic variant of MSO, called TMSO+zero, reduces to the emptiness problem for zero automata. We introduce a variant of zero automata called nonzero automata. We prove that for every zero automaton there is an equivalent nonzero automaton of quadratic size and the emptiness problem of nonzero automata is decidable, with complexity co-NP. These results imply that TMSO+zero has decidable satisfiability

    Complexity of Equivalence and Learning for Multiplicity Tree Automata

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    We consider the complexity of equivalence and learning for multiplicity tree automata, i.e., weighted tree automata over a field. We first show that the equivalence problem is logspace equivalent to polynomial identity testing, the complexity of which is a longstanding open problem. Secondly, we derive lower bounds on the number of queries needed to learn multiplicity tree automata in Angluin's exact learning model, over both arbitrary and fixed fields. Habrard and Oncina (2006) give an exact learning algorithm for multiplicity tree automata, in which the number of queries is proportional to the size of the target automaton and the size of a largest counterexample, represented as a tree, that is returned by the Teacher. However, the smallest tree-counterexample may be exponential in the size of the target automaton. Thus the above algorithm does not run in time polynomial in the size of the target automaton, and has query complexity exponential in the lower bound. Assuming a Teacher that returns minimal DAG representations of counterexamples, we give a new exact learning algorithm whose query complexity is quadratic in the target automaton size, almost matching the lower bound, and improving the best previously-known algorithm by an exponential factor

    Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

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    The topic of this paper is the analysis of stability for a class of switched linear systems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions
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