First-order spectra with one binary predicate

  • Arnaud Durand
  • Solomampionona Ranaivoson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 933)


The spectrum, Sp(ϕ), of a sentence ϕ is the set of cardinalities of finite structures which satisfy ϕ. We prove that any set of integers which is in Func 1 i.e. in the class of spectra of first-order sentences of type containing only unary function symbols is also in BIN1 i.e. in the class of spectra of first-order sentences of type involving only a single binary relation.

We give similar results for generalized spectra and some corollaries: in particular, from the fact that the large complexity class \(\mathop \cup \limits_c \)NTIME RAM (cn) is included in Func 1 for unary languages (n denotes the input integer), we deduce that the set of primes and many “natural” sets belong to BIN1


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Arnaud Durand
    • 1
  • Solomampionona Ranaivoson
    • 1
  1. 1.LAIACUniversité de CaenFrance

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