NDLI: Domino Games and Complexity

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Domino Games and Complexity

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Grdel, Erich
Copyright Year	1990
Abstract	Domino games which describe computations of alternating Turing machines in the same way as dominoes (tiling systems) encode computations of deterministic and nondeterministic Turing machines are considered. The domino games are two-person games in the course of which the players build up domino tilings of a square of prescribed size. Acceptance of an alternating Turing machine corresponds to a winning strategy for one playerthe number of moves in the game is the number of alternations of the Turing machine.Let $\operatorname{ATIME}(T(n), m)$ denote the class of all sets that are accepted by some alternating Turing machine in time $T(n)$ with at most m alternations. It is shown that any problem in such a complexity class can be reduced to the strategy problem for some domino game. In particular domino games which are complete in the classes $\Sigma_{m}^{p}$, and $\Pi_{m}^{p}$, of the polynomial time hierarchy are found. This corresponds to the approach of Savelsbergh and van Emde Boas and of Lewis and Papadimitriou, who have shown that the theory of NP-completeness may also be founded on a finite domino problem instead of the satisfiability problem for propositional formulae.Similar generalizations are possible for domino connectability problems: Domino thread games where the players build up a thread of dominoes are introduced; the first player wins if he can ultimately connect two given points. It is shown that a certain class of such games captures deterministic time complexity. In particular, games are found whose strategy problems are P-complete.In the last section applications to the complexity of simple prefix classes in logical theories are briefly discussed.
Starting Page	787
Ending Page	804
Page Count	18
File Format	PDF
ISSN	00975397
DOI	10.1137/0219055
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	19
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	domino problems Models of computation Modes of computation games alternating Turing machines Complexity of computation Complexity classes
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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