Logical Definability of NP Optimization Problems

: We investigate here NP optimization problems from a logical definability standpoint. We show that the class of optimization problems whose optimum is definable using first-order formulae coincides with the class of polynomially bounded NP optimization problems on finite structures. After this, we analyze the relative expressive power of various classes of optimization problems that arise in this framework. Some of our results show that logical definability has different implications for NP maximization problems than it has for NP minimization problems, in terms of both expressive power and approximation properties. To appear in Information and Computation. Research partially supported by NSF Grants CCR8905038 and CCR-9108631. y e-mail addresses: kolaitis@cse.ucsc.edu, thakur@cse.ucsc.edu z supersedes Technical report UCSC-CRL-90-48 1 Introduction and Summary of Results It is well known that optimization problems had a major influence on the development of the theory of NP-co..