In this note, we study under which conditions various sets (even easy ones) can be associated with a witnessing relation that is #P complete. We show a sufficient condition for an NP set to have such a relation. This condition applies also to many NP-complete sets, as well as to many sets in P .

We study the polynomial-time autoreducibility of NP-complete sets and obtain separations under strong hypotheses for NP. Assuming there is a p-generic set in NP, we show the following: • For every k ≥ 2, there is a k-T-complete set for NP that is k-T autoreducible, but is not k-tt autoreducible or (k − 1)-T autoreducible. • For every k ≥ 3, there is a k-tt-complete set for NP that is k-tt autor...

We consider two graph invariants that are used as a measure of nonplanarity: the splitting number of a graph and the size of a maximum planar subgraph. The splitting number of a graph G is the smallest integer k 0, such that a planar graph can be obtained from G by k splitting operations. Such operation replaces a vertex v by two nonadjacent vertices v1 and v2, and attaches the neighbors of v e...

L = {x such that x is an acceptable Riemann Hypothesis proof} is in NP and therefore, using a reduction, we can come up with a circuit C that takes as input x and outputs 1 if x is a proof for the Riemann Hypothesis or 0 otherwise. Our goal now is to design a pair of PPT machines (Enc,Dec) such that: 1. Enc(C,m) takes as input the circuit C and m ∈ {0, 1} and outputs a ciphertext e ∈ {0, 1}∗. 2...

This paper concerns the complexity analysis of the roommate problem and intern assignment problem with couples. These are two special cases of the matching problems known as stable matching. The roommate problem is that of assigning a set of people to rooms of exactly two occupants in accordance with the preferences of the members of the set. The intern assignment problem with couples is that o...

System BV is an extension of multiplicative linear logic (MLL) with the rules mix, nullary mix, and a self-dual, non-commutative logical operator, called seq. While the rulesmix and nullary mix extend the deductive system, the operator seq extends the language of MLL. Due to the operator seq, system BV extends the applications of MLL to those where sequential composition is crucial, e.g., concu...

We study the complexity of the Strategic Argumentation Problem for 2-player dialogue games where a player should decide what move (set of rules) to play at each turn in order to prove (disprove) a given thesis. We show that this is an NP-complete problem.

Finite state methods for natural language processing often require the construction and the intersection of several automata. In this paper we investigate the question of determining the best order in which these intersections should be performed. We take as an example lexical disambiguation in polarity grammars. We show that there is no efficient way to minimize the state complexity of these i...

System BV is an extension of multiplicative linear logic (MLL) with the rules mix, nullary mix, and a self-dual, non-commutative logical operator, called seq. While the rules mix and nullary mix extend the deductive system, the operator seq extends the language of MLL. Due to the operator seq, system BV extends the applications of MLL to those where sequential composition is crucial, e.g., conc...