80 research outputs found

    P(l)aying for Synchronization

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    Two topics are presented: synchronization games and synchronization costs. In a synchronization game on a deterministic finite automaton, there are two players, Alice and Bob, whose moves alternate. Alice wants to synchronize the given automaton, while Bob aims to make her task as hard as possible. We answer a few natural questions related to such games. Speaking about synchronization costs, we consider deterministic automata in which each transition has a certain price. The problem is whether or not a given automaton can be synchronized within a given budget. We determine the complexity of this problem. We also formulate a few open questions.Comment: Version 1 (by F\"odor Fominykh and Mikhail Volkov): 12 pages, 5 figures, close to the version published in the Proceedings of the 17th International Conference on Implementation and Application of Automata (LNCS 7381). Version 2: 19 pages, 7 figures, one of the problems left open in Version 1 solved, submitte

    Reachability of Consensus and Synchronizing Automata

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    We consider the problem of determining the existence of a sequence of matrices driving a discrete-time consensus system to consensus. We transform this problem into one of the existence of a product of the transition (stochastic) matrices that has a positive column. We then generalize some results from automata theory to sets of stochastic matrices. We obtain as a main result a polynomial-time algorithm to decide the existence of a sequence of matrices achieving consensus.Comment: Update after revie

    Synchronizing Words for Weighted and Timed Automata

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    The problem of synchronizing automata is concerned with the existence of a word that sends all states of the automaton to one and the same state. This problem has classically been studied for complete deterministic finite automata, with the existence problem being NLOGSPACE-complete. In this paper we consider synchronizing-word problems for weighted and timed automata. We consider the synchronization problem in several variants and combinations of these, including deterministic and non-deterministic timed and weighted automata, synchronization to unique location with possibly different clock valuations or accumulated weights, as well as synchronization with a safety condition forbidding the automaton to visit states outside a safety-set during synchronization (e.g. energy constraints). For deterministic weighted automata, the synchronization problem is proven PSPACE-complete under energy constraints, and in 3-EXPSPACE under general safety constraints. For timed automata the synchronization problems are shown to be PSPACE-complete in the deterministic case, and undecidable in the non-deterministic case

    Polynomial Time Decidability of Weighted Synchronization under Partial Observability

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    We consider weighted automata with both positive and negative integer weights on edges and study the problem of synchronization using adaptive strategies that may only observe whether the current weight-level is negative or nonnegative. We show that the synchronization problem is decidable in polynomial time for deterministic weighted automata

    The Formation of Stellar Clusters: Mass Spectra from Turbulent Molecular Cloud Fragmentation

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    Turbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass from the surrounding cloud material. This process is investigated, using numerical models of self-gravitating molecular cloud dynamics. Molecular cloud regions without turbulent driving sources, or where turbulence is driven on large scales, exhibit rapid and efficient star formation in a clustered mode, whereas interstellar turbulence that carries most energy on small scales results in isolated star formation with low efficiency. The clump mass spectrum of shock-generated density fluctuations in pure hydrodynamic, supersonic turbulence is not well fit by a power law, and it is too steep at the high-mass end to be in agreement with the observational data. When gravity is included in the turbulence models, local collapse occurs, and the spectrum extends towards larger masses as clumps merge together, a power-law description dN/dM ~ M^nu becomes possible with slope nu < -2. In the case of pure gravitational contraction, i.e. in regions without turbulent support, the clump mass spectrum is shallower with nu = -3/2. The mass spectrum of protostellar cores in regions without turbulent support and where turbulence is replenished on large-scales, however, is well described by a log-normal or by multiple power laws, similar to the stellar IMF at low and intermediate masses. In the case of small-scale turbulence, the core mass spectrum is too flat compared to the IMF for all masses.Comment: 10 pages including 2 figures, ApJ in press, a high-resolution preprint is available at http://www.ucolick.org/~ralf/Preprints/p13.abstract.htm

    Study of spread spectrum multiple access systems for satellite communications with overlay on current services

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    The feasibility of using spread spectrum techniques to provide a low-cost multiple access system for a very large number of low data terminals was investigated. Two applications of spread spectrum technology to very small aperture terminal (VSAT) satellite communication networks are presented. Two spread spectrum multiple access systems which use a form of noncoherent M-ary FSK (MFSK) as the primary modulation are described and the throughput analyzed. The analysis considers such factors as satellite power constraints and adjacent satellite interference. Also considered is the effect of on-board processing on the multiple access efficiency and the feasibility of overlaying low data rate spread spectrum signals on existing satellite traffic as a form of frequency reuse is investigated. The use of chirp is examined for spread spectrum communications. In a chirp communication system, each data bit is converted into one or more up or down sweeps of frequency, which spread the RF energy across a broad range of frequencies. Several different forms of chirp communication systems are considered, and a multiple-chirp coded system is proposed for overlay service. The mutual interference problem is examined in detail and a performance analysis undertaken for the case of a chirp data channel overlaid on a video channel

    Synchronizing automata over nested words

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    We extend the concept of a synchronizing word from deterministic finite-state automata (DFA) to nested word automata (NWA): A well-matched nested word is called synchronizing if it resets the control state of any configuration, i. e., takes the NWA from all control states to a single control state. We show that although the shortest synchronizing word for an NWA, if it exists, can be (at most) exponential in the size of the NWA, the existence of such a word can still be decided in polynomial time. As our main contribution, we show that deciding the existence of a short synchronizing word (of at most given length) becomes PSPACE-complete (as opposed to NP-complete for DFA). The upper bound makes a connection to pebble games and Strahler numbers, and the lower bound goes via small-cost synchronizing words for DFA, an intermediate problem that we also show PSPACE-complete. We also characterize the complexity of a number of related problems, using the observation that the intersection nonemptiness problem for NWA is EXP-complete
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