Robert E. Shostak. On the SUP-INF method for proving Presbuger formulas. Journal of the Association for Computing Machinery, 24(4):529--543, October 1977. 22  Home/Search   Document Not in Database   Summary   Related Articles

....from some class of functions, rela2 tions and types. It is then natural to focus on the problem of improving on the average cost of decision problems that are in general intractable. In this paper we examine two sublanguages, fragments of set theory [FOS80, Pol87] and integer linear programming [Dav57, Coo71, Coo72, Sho77, CZ93] used in the Davis Schwartz approach to correct program technology. Several ways of dealing with the seeming intractability of these languages have been explored. For example, we can search for tiny sublanguages whose decision problem has polynomial time complexity in the worst case [Pra77, ....

....id j ILP ILP According to Oppen [Opp75] by algorithms of Hilbert Bernays [HB68, pp. 366 375] and Cooper [Coo71, Coo72] it is known that satisfiability of Presburger arithmetic can be solved in no worse than 2 2 2 n time steps for inputs of size n for mixed quantifiers. According to Shostak [Sho77], Cooper s algorithm rarely exhibits the worst case. Oppen has observed that the satisfiability problem for FPILP is NP complete. The problem of deciding the satisfiability of purely existentially quantified conjuncts OE of literals of the form x y Gamma c, x c or x = y is, on the other hand, ....

Robert E. Shostak. On the SUP-INF method for proving Presbuger formulas. Journal of the Association for Computing Machinery, 24(4):529--543, October 1977. 22

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