Jan Johannsen

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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)
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 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)