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This paper presents a method for the synthesis of a one-dimensional linear hybrid cellula from a given irreducible polynomial. A detailed description of the algorithm is given, toget the theoretical background. It is shown that two CA exist for each irreducible polynomial, open CA existence conjecture. An in-depth example of the synthesis is presented,… (More)

Many applications call for exhaustive lists of strings subject to various constraints , such as inequivalence under group actions. A k-ary necklace is an Ž. equivalence class of k-ary strings under rotation the cyclic group. A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present… (More)

This letter is a supplement of the table of the minimal cost one-dimensional linear hybrid cellular automata with the maximum length cycle

The Graph Minor Theorem of Robertson and Seymour establishes nonconstructively that many natural graph properties are characterized by a nite set of forbidden sub-structures, the obstructions for the property. We prove several general theorems regarding the computation of obstruction sets from other information about a family of graphs. The methods can be… (More)

For the family of graphs with xed-size vertex cover k, we present all of the forbidden minors (obstructions), for k up to ve. We derive some results, including a practical nite-state recognition algorithm, needed to compute these obstructions.

Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. In this paper we characterize several families of graphs with small feedback sets, namely k 1-Feedback Vertex Set, k 2-Feedback Edge Set and (k 1 ,k 2){Feedback Vertex/Edge Set, for small integer parameters k 1 and k 2. Our… (More)

Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals. In this paper, we describe a general-purpose method for nding obstructions by using a bounded treewidth (or… (More)

We described a simple algorithm running in linear time for each fixed constant, k, that either establishes that the pathwidth of a graph G is greater than k, or finds a path-decomposition of G of width at most O(zk). This provides a simple proof of the result by Bodlaender that many families of graphs of bounded pathwidth can be recognized in linear time.

The paper studies theoretical aspects of one dimensional linear hybrid cellular automata field. General results concerning the characteristic polynomials of such automata are pre synthesis algorithm for determining such a linear hybrid cellular automaton with a specific polynomial is given, along with empirical results and a theoretical analysis. Cyclic… (More)