Nondeterministic functions and the existence of optimal proof systems

We provide new characterizations of two previously studied questions on nondeterministic function classes: Q1: Do nondeterministic functions admit efficient deterministic refinements? Q2: Do nondeterministic function classes contain complete functions? We show that Q1 for the class is equivalent to the question whether the standard proof system for SAT is p-optimal, and to the assumption that every optimal proof system is p-optimal. Assuming only the existence of a p-optimal proof system for SAT, we show that every set with an optimal proof system has a p-optimal proof system. Under the latter assumption, we also obtain a positive answer to Q2 for the class . An alternative view on nondeterministic functions is provided by disjoint sets and tuples. We pursue this approach for disjoint -pairs and its generalizations to tuples of sets from and with disjointness conditions of varying strength. In this way, we obtain new characterizations of Q2 for the class . Question Q1 for is equivalent to the question of whether every disjoint -pair is easy to separate. In addition, we characterize this problem by the question of whether every propositional proof system has the effective interpolation property. Again, these interpolation properties are intimately connected to disjoint -pairs, and we show how different interpolation properties can be modeled by -pairs associated with the underlying proof system

A kutya elülső végtag csontvázának és artériás rendszerének 3D-s modell

Az anatómia oktatásban elsődlegesen kétdimenziós ábrákat használnak a képletek személtetésére, viszont a tanulóknak ezek alapján nagyon nehéz értelmezni a szervezet térbeni felépítését. Ennek a problémának a megoldására a kereskedelmi forgalomban és az interneten hozzáférhetőek különböző számítógépes modellek, amelyek grafikai úton, anatómiai könyvek ábrái alapján készültek, és felbontásuk, részletességük sem megfelelő. Ennek a tanulmánynak az volt a célja, hogy eredeti helyzetükben, realisztikusan és nagy felbontásban mutassa be a csontok és a főbb artériák viszonyát a kutya mellső végtagján

Permanent Does Not Have Succinct Polynomial Size Arithmetic Circuits of Constant Depth

Abstract. We show that over fields of characteristic zero there does not exist a polynomial p(n) and a constant-free 1 succinct arithmetic circuit family {Φn}, where Φn has size at most p(n) and depth O(1), such that Φn computes the n × n permanent. A circuit family {Φn} is succinct if there exists a nonuniform Boolean circuit family {Cn} with O(log n) many inputs and size n o(1) such that that Cn can correctly answer direct connection language queries about Φn- succinctness is a relaxation of uniformity. To obtain this result we develop a novel technique that further strengthens the connection between black-box derandomization of polynomial identity testing and lower bounds for arithmetic circuits. From this we obtain the lower bound by explicitly constructing a hitting set against arithmetic circuits in the polynomial hierarchy.

On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System

We investigate the computational complexity of counting the Hilbert basis of a homogeneous system of linear Diophantine equations. We establish lower and upper bounds on the complexity of this problem by showing that counting the Hilbert basis is #P-hard and belongs to the class #NP. Moreover, we investigate the complexity of variants obtained by restricting the number of occurrences of the variables in the system