Showing papers on "Continuous automaton published in 1987"

Formal Language Characterization of Cellular Automaton Limit Sets.

Abstract: A formal language description of one-d imensional cellu lar automata limit sets is given, an d a series of examples illustrating several degrees of complexity are constructed. The undecidability of membership of a string in the limi t set of a cellu lar automaton ru le is proven.

Diversity-based inference of finite automata

Abstract: We present a new procedure for inferring the structure of a finitestate automaton (FSA) from its input/output behavior, using access to the automaton to perform experiments. Our procedure uses a new representation for FSA's, based on the notion of equivalence between testa. We call the number of such equivalence classes the diversity of the automaton; the diversity may be as small as the logarithm of the number of states of the automaton. The size of our representation of the FSA, and the running time of our procedure (in some case provably, in others conjecturally) is polynomial in the diversity and ln(1/e), where e is a given upper bound on the probability that our procedure returns an incorrect result. (Since our procedure uses randomization to perform experiments, there is a certain controllable chance that it will return an erroneous result.) We also present some evidence for the practical efficiency of our approach. For example, our procedure is able to infer the structure of an automaton based on Rubik's Cube (which has approximately 1019 states) in about 2 minutes on a DEC Micro Vax. This automaton is many orders of magnitude larger than possible with previous techniques, which would require time proportional at least to the number of global states. (Note that in this example, only a small fraction (10-14) of the global states were even visited.)

RAP1, a Cellular Automaton Machine for Fluid Dynamics.

Abstract: A bstra ct. RAP l is a spec ial pur pose comp uter built to st udy lat tice gas models. It allows the simulation of any model using less t ha n 16 bits p er node , and interacti ons restricted to first and second nearest neighb ors on a 256 x 512 square lat t ice. T he t ime evolu t ion of the automaton is displayed in real time on a color monitor at a sp eed of 50 fr ames per second. 1. I nt roduction T he concept of cellu lar automata was introduced in the early fift ies by von Neumann and U lam 11] to st ud y the be havior and the organization of complex systems. A cellular automaton (CA) is a set of identical processors located on a regu lar lat tice and with limited connections with t he ir neighbors. For each time ste p, th e CA is described by the values of t he states of all the pro cessors. At time t + 1, all t he pro cessors comp ute in parallel t he ir new state as a given function of t heir st ate and t hose of t he con nected p ro-cessors at time t , Wolfram [2] has shown t hat very simp le one-d imensional CA wit h one-b it int ernal states may give extremely complicated be hav iors, as soon as each cell is connected to its first-and second-nearest neighb ors and its time evolut ion is given by a Boolean funct ion chosen within t he suitable set of Boolean functi ons of five Boolean var iables. T he CAM mac hines built at MIT by T. Toffoli [3] played a pr ominent par t in t he int erest for CA during the las t five years. These machines demonst rated t hat cheap , but very powerful, spe cia l-purpose comp uters can be buil t to st udy a wide class of CA. T hey have also shown the impact of dir ect visualization on t he study of very complex phe nomena. Duri ng the same t ime, several attempts were done in t he phys icist com-mu nity to find simp le ways to descr ibe and st udy the motion of a collection of int eracting particles [4,5]. In …

The Free Energy Concept in Cellular Automaton Models of Solid-Solid Phase Transitions.

Abstract: Landau theories can describe charac teristic featu res of shape memory alloys associated with their thermoe lastic martensitic phase transformation. Such theories, based on a continuously variable free energy function F(e,T), explain global behaviour satisfactor ily but neg lect microscopic aspects of the lattice change where t he order parameter e can only switch between a few fixed values . In a corresponding ceJ1ular type theory, we re p lace the cont inuo us F(e, T ) by a discrete set of functions F;, each depending on contin uous global variab les such as temperature T and stress X. The processing algorithm mi nimi zes for each cell the sum of F; and the in terfac e energies with its neighbours. At a fixed (T, Xl-condition, this process is equivalent to a cellular automaton transition rule. The simple case of a 3-state, one-dimensional martensite model is discussed in detail ; chan ges for two-dimens ional extensions are outlined.

The hierarchical structure of graph searches

Abstract: Given a graph B , we show the existenee of a universal automaton U which “searches” B. U is universal in the sense that any automaton which searches B behaves as a subautomaton of U . Further, U is naturally filtered in a manner suggestive of hierarchical search depth: level 1 corresponds to simple rules for moving on B , level 2 to “meta-rules,” and so on. We show that if M is any finite state automaton which searches B , then M can in fact be embedded in some finite level U n of U . This leads naturally to a definition of “depth” of an arbitrary automaton which searches B , and we give several examples of such automata with varying depth. This notion of depth is independent of the state space structure of M . We further describe a resulting strategy for the construction of evolutionary learning systems which learn structural control hierarchies, based on our model of the universal automaton.