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Journals and Conferences
The problem of converting deterministic finite automata into (short) regular expressions is considered. It is known that the required expression size is 2 in the worst case for infinite languages, and for finite languages it is n log n) and n, if the alphabet size grows with the number of states n of the given automaton. A new lower bound method based on… (More)
Two distinct proofs of an exponential separation between regular resolution and unrestricted resolution are given. The previous best known separation between these systems was quasi-polynomial.
An exponential lower bound for the size of tree-like Cutting Planes refutations of a certain family of CNF formulas with polynomial size resolution refutations is proved. This implies an exponential separation between the tree-like versions and the dag-like versions of resolution and Cutting Planes. In both cases only superpolynomial separations were known… (More)
We prove an exponential lower bound for tree-like Cutting Planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential separation between tree-like and dag-like proofs for both CuttingPlanes and resolution; in both cases only superpolynomial separations were known before [30, 20, 10]. In order to prove… (More)
We show that the satisfiability problem for CTL, the branching time logic that allows boolean combinations of path formulas inside a path quantifier but no nesting of them, is 2-EXPTIME-hard. The construction is inspired by Vardi and Stockmeyer’s 2-EXPTIME-hardness proof of CTL∗’s satisfiability problem. As a consequence, there is no subexponential… (More)
We deene an extension R 0 2 of the bounded arithmetic theory R 0 2 and show that the class of functions b 1-deenable in R 0 2 coincides with the computational complexity class TC 0 of functions computable by polynomial size, constant depth threshold circuits.
We define theories of Bounded Arithmetic characterizing classes of functions computable by constantdepth threshold circuits of polynomial and quasipolynomial size. Then we define certain second-order theories and show that they characterize the functions in the Counting Hierarchy. Finally we show that the former theories are isomorphic to the latter via the… (More)
Using a notion of real communication complexity recently introduced by J. Kraj cek, we prove a lower bound on the depth of monotone real circuits and the size of monotone real formulas for st-connectivity. This implies a super-polynomial speed-up of dag-like over tree-like Cutting Planes proofs.
We deene theories of Bounded Arithmetic characterizing classes of functions computable by constant-depth threshold circuits of polynomial and quasipoly-nomial size. Then we deene certain second-order theories and show that they characterize the functions in the Counting Hierarchy. Finally we show that the former theories are isomorphic to the latter via the… (More)