Searching for authors named "Cristopher Moore" – sorted by Relevance.
63 documents found, showing 1 through 10.
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Predicting Non-linear Cellular Automata Quickly by Decomposing Them into Linear Ones
- …We show that a wide variety of non-linear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depth O(log 2 t) using gates with binary inputs, or O(log t) depth if "sum mod p" gates with an unbounded number of inpu…
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Generalized one-sided shifts and maps of the interval
- …Abstract. We consider a generalization of the one-sided shift, suitable for describing a certain class of maps in the interval that preserve a Cantor set. We show that if such a map is single-valued, it has a finite Markov partition (i.e. that its symbolic dynamics is regular), but if it is multiple…
- Cited by 2 (0 self) – Add To MetaCart
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Recursion Theory on the Reals and Continuous-time Computation
- …We define a class of recursive functions on the reals analogous to the classical recursive functions on the natural numbers, corresponding to a conceptual analog computer that operates in continuous time. This class turns out to be surprisingly large, and includes many functions which are uncomp…
- Cited by 58 (4 self) – Add To MetaCart
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Quantum Circuits: Fanout, Parity, and Counting
- …We propose definitions of QAC0, the quantum analog of the classical class AC0 of constant-depth circuits with AND and OR gates of arbitrary fan-in, and QACC0[q], where n-ary MODq gates are also allowed. We show that it is possible to make a `cat' state on n qubits in constant depth if and only if we…
- Cited by 9 (1 self) – Add To MetaCart
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Quasi-Linear Cellular Automata
- …Simulating a cellular automaton (CA) for t time-steps into the future requires t 2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed linear because they obey a principle of superposition. This allows them to be predicte…
- Cited by 10 (4 self) – Add To MetaCart
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Dynamical Recognizers: Real-time Language Recognition by Analog Computers
- …We consider a model of analog computation which can recognize various languages in real time. We encode an input word as a point in R d by composing iterated maps, and then apply inequalities to the resulting point to test for membership in the language. Each class of maps and inequalities, suc…
- Cited by 42 (4 self) – Add To MetaCart
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Majority-Vote Cellular Automata, Ising Dynamics, and
- …We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single spin-flip dynamics of the Ising model at zero temperature. We sh…
- Cited by 18 (7 self) – Add To MetaCart
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Majority-Vote Cellular Automata, Ising Dynamics, and
- …We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single spin-flip dynamics of the Ising model at zero temperature. We show t…
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Commuting Cellular Automata
- …. We study the algebraic conditions under which two onedimensional cellular automata can commute. We show that if either rule is permutive, i.e. one-to-one in its leftmost and rightmost inputs, then the other rule can be written in terms of it; if either rule is a group, then the other is linear…
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Hard Tiling Problems with Simple Tiles
- …It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show that Monotone 1-in-3 Sati…
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