Games with a Uniqueness Property

Aida, Shin; Crasmaru, Marcel; Regan, Kenneth W.; Watanabe, Osamu

doi:10.1007/3-540-45841-7_32

Cited by 2 publications

(4 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [ACRW02], UAP was characterized as the class of languages that polynomialtime many-one reduce to the following promise problem GUQBF :…”

Section: Corollary 1 Uap Is Closed Under All Boolean Operationsmentioning

confidence: 99%

“…We remark that coming into or exiting a sub-game G i may give two consecutive moves to one of the players, but (i) this does not matter to the above analysis, (ii) it is easy to avoid beforehand by modifying M A and M to avoid this, and (iii) it is fixable afterwards by padding methods used here and in results of [ACRW02] quoted below anyway.…”

Section: Introductionmentioning

confidence: 99%

“…The protocol for converting general alternating-P (i.e., PSPACE) computations into plays of globally-unique games in [ACRW02] involves exponential backtracking-it cannot be improved to polynomial unless PSPACE collapses into UAP, hence into SPP, thence into ⊕P and PP, which is generally disbelieved. The only advantage in our setting is that the individual games G i already have global uniqueness of winning strategies.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Protocol for Serializing Unique Strategies

Crasmaru

Glaßer

Regan

et al. 2004

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. We devise an efficient protocol by which a series of twoperson games Gi with unique winning strategies can be combined into a single game G with unique winning strategy, even when the result of G is a non-monotone function of the results of the Gi that is unknown to the players. In computational complexity terms, we show that the class UAP of Niedermeier and Rossmanith [NR98] of languages accepted by unambiguous polynomial-time alternating TMs is self-low, i.e., UAP UAP = UAP. It follows that UAP contains the Graph Isomorphism problem, nominally improving the problem's classification into SPP by Arvind and Kurur [AK02] since UAP is a subclass of SPP [NR98]. We give some other applications, oracle separations, and results on problems related to unique-alternation formulas.

show abstract

“…In [ACRW02], UAP was characterized as the class of languages that polynomialtime many-one reduce to the following promise problem GUQBF :…”

Section: Corollary 1 Uap Is Closed Under All Boolean Operationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation