In this talk, I will discuss an approach to the P = NP question via the correspondence between logic and complexity. The main focus will be on the possible use of Ehrenfeucht-Fraı̈ssé games.

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While playing against Deep Blue, Kasparov reported feeling an ’alien intelligence’ across the board: something that was undoubtedly thinking, but not in the way that any human thinker would. Kasparov feels he is defending the honor of the human race. If cloning a single sheep can put the leaders of the Western world into such a tizzy, one wonders how will they react to the prospect of inhuman m...

Let P be a polytope satisfying that each row of the defining matrix has at most one positive entry. Determining whether there is an integer point in P is known to be an NP-complete problem. By introducing an integer labeling rule on an augmented set and applying a triangulation of the Euclidean space, we develop in this paper a variable dimension method for computing an integer point in P. The ...

We introduce the NP-complete problem 3SATN and extend Tovey’s results to a classification theorem for this problem. This classification theorem leads us to generalize the concept of truth assignments for SAT to aggressive truth assignments for 3SATN . All these aggressive truth assignments are pseudo-algorithms. We combine algorithm, pseudo-algorithm and diagonalization method to study the comp...

Children at the age of 3 or less invariably got the answer wrong and assumed that Maxi would look for the chocolate in the green cupboard where they knew it was. Even children aged 4-5 had only a one third chance of correctly answering this question or an analgous question involving Maxi and his brother (who also wants the chocolate and whom Maxi wants to deceive). Children aged 6 or more were ...

In this paper we introduce a variant of membrane systems with elementary division and without charges. We allow only elementary division where the resulting membranes are identical; we refer to this using the biological term symmetric division. We prove that this model characterises P. This result characterises the power of a class of membrane systems that fall under the so called P conjecture ...

We prove that a pair of polynomially samplable distributions are statistically indistinguishable if and only if no polynomial size circuits relative to NP sets (P NP nu-distinguishers) can tell them apart. As one application of this observation, we classify \zero-knowledge" notions that are used for interactive protocols.