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- W2000860116 abstract "Abstract Mostowski [11] shows that if a structure has a decidable theory, then its weak direct power has one as well; his proof however never produces decision procedures which are elementary recursive. Some very general results are obtained here about the nature of the weak direct power of a structure, which in most cases lead to elementary recursive decision procedures for weak direct powers of structures which themselves have elementary recursive procedures. In particular, it is shown that 〈 N *, +〉, the weak direct power of 〈 N , +〉, can be decided in space for some constant c . As corollaries, the same upper bound is obtained for the theory of the structure 〈 N + , ·〉 of positive integers under multiplication, and for the theory of finite abelian groups. Fischer and Rabin [7] have shown that the theory of 〈 N ,* +〉 requires time even on nondeterministic Turing machines." @default.
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- W2000860116 date "1976-09-01" @default.
- W2000860116 modified "2023-09-27" @default.
- W2000860116 title "On the complexity of the theories of weak direct powers" @default.
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- W2000860116 doi "https://doi.org/10.1017/s0022481200051136" @default.
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