, Volume 23, Issue 3, pp 325-356

The complexity of combinatorial problems with succinct input representation

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Summary

Several languages for the succinct representation of the instances of combinatorial problems are investigated. These languages have been introduced in [20, 2] and [5] where it has been shown that describing the instances by these languages causes a blow-up of the complexities of some problems. In the present paper the descriptional power of these languages is compared by estimating the complexities of some combinatorial problems in terms of completeness in suitable classes of the “counting polynomial-time hierarchy” which is introduced here. It turns out that some of the languages are not comparable, unless P=NP Some problems left open in [2] are solved.

A preliminary version of this paper appeared in the proceedings of the Second Frege Conference held in September 1984 in Schwerin (GDR), see [24]