Hierarchically and 1-Dimensional Periodically Specified Generalized CNF Satisfiability Problems with Applications1
نویسندگان
چکیده
We study the complexity of various combinatorial problems when instances are specified using one of the following succinct specifications: (1) the 1-dimensional finite periodic narrow specifications of Ford et al. and Höfting and Wanke [FF58, HW95]; (2) the 1-dimensional finite periodic narrow specifications with explicit boundary conditions of Gale [Ga59]; (3) the 2-way infinite 1-dimensional periodic narrow specifications of Orlin et al. [Or82a]; and (4) the hierarchical specifications of Lengauer et al. [LW87a]. The following general results are obtained. 1. Assuming P 6= PSPACE, we characterize completely the polynomial time solvability of the generalized CNF satisfiability problems of Schaefer [Sc78], when instances are specified succinctly as in (1), (2), (3) or (4) above. 2. As applications of our results, we present several new PSPACE-hardness results and give polynomial time algorithms for problems specified as in (1), (2), (3) or (4) above. The results and the ideas given here and in [MH+94, MH+96a] significantly extend the known hardness/easiness results in [LW92, Or82a, RH93].
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