kbstr act We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fan-in circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MOD, where p is a prime require Ezp

In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions

of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing

We give improved lower bounds for the size of small depth circuits computing several functions. In particular we prove almost optimal lower bounds for the size of parity circuits. Fur-ther we show that there are functions computable in polynomial size and depth k but requires ex-ponential size

SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logic-level description of a sequential circuit, it produces an optimized net-list in the target technology while preserving the sequential input

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We prove the first exponential lower bound on the size of any depth 3 arithmetic circuit with unbounded fanin computing an explicit function (the determinant) over an arbitrary finite field. This answers an open problem of [N91] and [NW95] for the case of finite fields. We intepret here arithmetic

We propose a new method to quickly and accurately predict 3D positions of body joints from a single depth image, using no temporal information. We take an object recognition approach, designing an intermediate body parts representation that maps the difficult pose estimation problem into a simpler

;enyi's nonmonotone result [Imm88, Sze87] that NL = co-NL; this is a simple extension of the monotone circuit depth lower bound of Karchmer and Wigderson [KW90] for st-connectivity. We also consider mBWBP (monotone bounded width branching programs) and study the question of whether mBWBP is properly contained

Symbolic Model Checking [3, 14] has proven to be a powerful technique for the verification of reactive systems. BDDs [2] have traditionally been used as a symbolic representation of the system. In this paper we show how boolean decision procedures, like Stalmarck's Method [16] or the Davis