Sam M. Kim

Some results concerning linear iterative (systolic) arrays

Abstract Characterizations of various types of linear iterative (systolic) arrays in terms of single processor sequential machines are given. Using these characterizations, new or improved results concerning the properties, power, and limitations of the different linear array models are proved. For example, a speed-up theorem is proved that is stronger than what has previously appeared in the literature and, moreover, works for arrays with one-way communication lines. Also investigated are the effects of augmenting the array with a supplemental control mechanism called global control. It is shown that in many cases arrays with global control can be simulated in real-time by arrays without global control. The result remains true even if one of the processors is augmented by a stack. Cases are also exhibited where the addition of global control makes the array strictly more powerful, even if the control lines are restricted to only a few processors of the array.

Sequential Machine Characterizations of Trellis and Cellular Automata and Applications

We look at a simple, but general model, of a systolic system called a trellis automaton (TA). A TA is equivalent in computational power to a one-dimensional unbounded cellular automaton (CA), a model of parallel computation which has been studied extensively in the literature. Different varieties of TA’s are equivalent to corresponding variations of CA’s. We present, for the first time, sequential machine characterizations of TA’s (CA’s). The sequential machines are useful and powerful tools for investigating properties of TA’s (CA’s). They ar easy to program because, unlike the parallel models, one does not have to deal with the problem of synchronization. Several applications are given. In particular, we prove a new speed-up theorem which is stronger than what has previously been shown.

A polynomial time algorithm for the local testability problem of deterministic finite automata

The local testability problem of deterministic finite automata is investigated. A locally testable language is a language with the property that, for some nonnegative integer k, whether or not a word w is in the language depends on (1) the prefix and suffix of w of length k, and (2) the set of substrings of w length k+1, without regard to the order in which these substrings occur. The local testability problem is, given a deterministic finite automation, to decide whether or not it accepts a locally testable language. The authors present an O(n/sup 2/) time algorithm for the local testability problem based on two simple properties that characterize locally testable automata. >

Fast parallel language recognition by cellular automata

Abstract We look at linear cellular automata (CAs) which accept an input if and only if at some time during the computation all the processors in the array are in accepting states. We prove that there are noncontext-free languages that are accepted by CAs in O(log n) time. Moreover, this is the best possible since o(log n) time CAs can accept only regular sets. We show that one-way CAs operating in T(n) time can be simulated by CAs in 1 2 (T(n) + 1) time. As a corollary, CAs can accept the linear, Dyck, and bracketed context-free languages in 1 2 (n + 1) time, which is again optimal. We also study CAs with other modes of acceptance and derive results concerning speed-up, hierarchy, etcetera.

Computing the Order of a Locally Testable Automaton

A locally testable language is a language with the property that, for some positive integer

Computational Modeling for Genetic Splicing Systems

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Designing Systolic Algorithms Using Sequential Machines

, whether or not a string

A Polynomial Time Algorithm for the Local Testability Problem of Deterministic Finite Automata

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An Upper Bound on the Order of Locally Testable Deterministic Finite Automata

is in the language depends on (1) the prefix and suffix of

Characterizations of multihead finite automata

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