Logical Decision Problems and Complexity of Logic Programs

Article type: Research Article

Authors: Börger, Egon^a | Löwen, Ulrich^b

Affiliations: [a] Dipartimento di Informatica, Universita di Pisa, Corso Italia 40, 56100 Pisa, Italy | [b] Abteilung Informatik, Universität Dortmund, 4600 Dortmund, F.R.G.

Abstract: We survey and give new results on logical characterizations of complexity classes in terms of the computational complexity of decision problems of various classes of logical formulas. There are two main approaches to obtain such results: The first approach yields logical descriptions of complexity classes by semantic restrictions (to e.g. finite structures) together with syntactic enrichment of logic by new expressive means (like e.g. fixed point operators). The second approach characterizes complexity classes by (the decision problem of) classes of formulas determined by purely syntactic restrictions on the formation of formulas.

DOI: 10.3233/FI-1987-10102

Journal: Fundamenta Informaticae, vol. 10, no. 1, pp. 1-33, 1987