The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Formal languages and their relation to automata
Formal languages and their relation to automata
Randomness and completeness in computational complexity
Randomness and completeness in computational complexity
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In this paper we give a complete problem in DSPACE(n). The problem is whether there exists a cycle in the connected component containing (o,o,...,o) in the graph Gp of the zeroes of a polynomial P over GF(2) under a suitable natural coding. Hence the deterministic space complexity of this problem is O(n) but not o(n). We give as well several problems for which we can obtain very close upper and lower deterministic space bounds. For example, the deterministic space complexity to determine whether there exists a cycle in the graph of the set of assignments satisfying a Boolean formula is O(n/log n) but not o(n/log2n).