Showing papers by "Phokion G. Kolaitis published in 1993"
Proceedings Article•
01 Jan 1993
TL;DR: In this article, a study of polynomial-time optimization from the perspective of descriptive complexity theory is initiated, and it is established that the class of problems with ordered finite structures as instances can be characterized in terms of the stage functions of positive first-order formulas, i.e., the functions that compute the number of distinct stages in bottom-up evaluation of the least fixpoints of such formulas.
Abstract: A study of polynomial-time optimization from the perspective of descriptive complexity theory is initiated. It is established that the class of polynomial-time and polynomially bounded optimization problems with ordered finite structures as instances can be characterized in terms of the stage functions of positive first-order formulas, i.e., the functions that compute the number of distinct stages in the bottom-up evaluation of the least fixpoints of such formulas. After this, the stage functions of several first-order formulas whose least fixpoints form natural p-complete problems are studied, and it is shown that they are not NC-approximate within any factor of the optimum, unless P=NC. Finally, it is proved that certain polynomial-time optimization problems are complete with respect to a new kind of restricted reductions that preserve parallel approximability and are definable using quantifier-free formulae.<>
4 citations
18 May 1993
TL;DR: It is proved that certain polynomial-time optimization problems are complete with respect to a new kind of restricted reductions that preserve parallel approximability and are definable using quantifier-free formulae.
Abstract: A study of polynomial-time optimization from the perspective of descriptive complexity theory is initiated. It is established that the class of polynomial-time and polynomially bounded optimization problems with ordered finite structures as instances can be characterized in terms of the stage functions of positive first-order formulas, i.e., the functions that compute the number of distinct stages in the bottom-up evaluation of the least fixpoints of such formulas. After this, the stage functions of several first-order formulas whose least fixpoints form natural p-complete problems are studied, and it is shown that they are not NC-approximate within any factor of the optimum, unless P=NC. Finally, it is proved that certain polynomial-time optimization problems are complete with respect to a new kind of restricted reductions that preserve parallel approximability and are definable using quantifier-free formulae. >
3 citations