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An O(n2) space representation for permutation groups of degree n is presented. The representation can be constructed in time O(n5), and supports fast membership testing. Applications of the representation to the generation of systems of coset representatives, and of complete block systems, are discussed.
Deterministic exponential lower time bounds are obtained for analyzing monadic recursion schemes, multi-variable recursion schemes, and recursive programs. The lower bound for multivariable recursion schemes holds for any domain of interpretation with at least two elements. The lower bound for recursive programs holds for any recursive programming language with a nontrivial predicate test (i.e. a...
A permutation group on n letters may always be represented by a small set of generators, even though its size may be exponential in n. We show that it is practical to use such a representation since many problems such as membership testing, equality testing, and inclusion testing are decidable in polynomial time. In addition, we demonstrate that the normal closure of a subgroup can be computed in...
We introduce a network of processing elements, the cube-connected-cycles (CCC), complying with the present technological constraints of VLSI design. By combining the principles of parallelism and pipelining, the CCC can emulate the cube-connected machine with no significant degradation of performance but with a much more compact structure. We describe in detail how to program the CCC for efficiently...
In this note we show that the tape bounded complexity classes of languages over single letter alphabets are closed under complementation. We then use this result to show that there exists an infinite hierarchy of tape bounded complexity classes of sla languages between log n and log log n tape bounds. We also show that every infinite sla language recognizable on less than log n tape has infinitely...
Decision procedures for validity in intuitionistic propositional calculus and modal propositional calculus are given which require a running time proportional to a polynomial in the length of the formula on a nondeterministic Turing machine. Using a theorem of Cook's and well-known transformations from intuitionistic to classical and modal to intuitionistic logics, the validity problem for intuitionistic...
Let Σ be a finite alphabet, Σ* the free monoid generated by Σ and |x| the length of x ε Σ*. For any integer k ≥ 0, fk(x)(tk (x)) is x if |x| ≪ k+1, and it is the prefix (suffix) of x of length k, otherwise. Also let mk+1 (x) = {v|x = uvw and |v| = k+1}. For x,y ε Σ* define x ∼k+1y iff fk(x) = fk(y), tk(x) = tk(y) and mk+1(x) = mk+1 (y). The relation ∼k+1 is a congruence of finite index over Σ*. An...
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