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A logic for constantdepth circuits
 Information and Control
, 1984
"... Consider a family of boolean circuits C~, C2,..., C,,..., constructed by some uniform, effective procedure operating on input n. Such a procedure provides a concise representation of a family of parallel algorithms for computing boolean values. A formula of firstorder logic may also be viewed as a ..."
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Cited by 18 (3 self)
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, constantdepth, unboundedfanin circuits constructed by Turing machines of bounded computational complexity. © 1984 Academic Press, Inc. Several papers (Chandra et al., 1983a; Chandra et al., 1982; Chandra et al., 1983b; Furst et al., 1981; Sipser, 1983) have recently dealt with the
Definability by constantdepth polynomialsize circuits
 Information and Control
, 1986
"... A function of boolean arguments is symmetric if its value depends solely on the number of l's among its arguments. In the first part of this paper we partially characterize those symmetric functions that can be computed by constantdepth polynomialsize sequences of boolean circuits, and discus ..."
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Cited by 18 (0 self)
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to circuits recognizing firstorder structures. By imposing fairly natural restrictions we develop a circuit model with precisely the power of firstorder logic: a class of structures is firstorder definable if and only if it can be recognized by a constantdepth polynomialtime sequence of such circuits
On the ConstantDepth Complexity of kClique
"... We prove a lower bound of ω(n k/4) on the size of constantdepth circuits solving the kclique problem on nvertex graphs (for every constant k). This improves a lower bound of ω(n k/89d2) due to Beame where d is the circuit depth. Our lower bound has the advantage that it does not depend on the cons ..."
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Cited by 13 (3 self)
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We prove a lower bound of ω(n k/4) on the size of constantdepth circuits solving the kclique problem on nvertex graphs (for every constant k). This improves a lower bound of ω(n k/89d2) due to Beame where d is the circuit depth. Our lower bound has the advantage that it does not depend
SIS: A System for Sequential Circuit Synthesis
, 1992
"... SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logiclevel description of a sequential circuit, it produces an optimized netlist in the target technology while preserving the sequential inputoutput b ..."
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Cited by 527 (44 self)
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SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logiclevel description of a sequential circuit, it produces an optimized netlist in the target technology while preserving the sequential input
A Theory of Diagnosis from First Principles
 ARTIFICIAL INTELLIGENCE
, 1987
"... Suppose one is given a description of a system, together with an observation of the system's behaviour which conflicts with the way the system is meant to behave. The diagnostic problem is to determine those components of the system which, when assumed to be functioning abnormally, will explain ..."
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Cited by 1120 (5 self)
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, will explain the discrepancy between the observed and correct system behaviour. We propose a general theory for this problem. The theory requires only that the system be described in a suitable logic. Moreover, there are many such suitable logics, e.g. firstorder, temporal, dynamic, etc. As a result
A theory of timed automata
, 1999
"... Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of ..."
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Cited by 2651 (32 self)
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using finitely many realvalued clock variables. Automated analysis of timed automata relies on the construction of a finite quotient of the infinite space of clock valuations. Over the years, the formalism has been extensively studied leading to many results establishing connections to circuits
Symbolic Model Checking: 10^20 States and Beyond
, 1992
"... Many different methods have been devised for automatically verifying finite state systems by examining stategraph models of system behavior. These methods all depend on decision procedures that explicitly represent the state space using a list or a table that grows in proportion to the number of st ..."
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Cited by 758 (41 self)
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to symbolic model checking by discussing how it can be used to verify a simple synchronous pipeline circuit.
ConstantDepth Quantum Circuits with Gates for Addition
"... Abstract. We investigate a class QNC 0 (ADD) that is QNC 0 with gates for addition of two binary numbers, where QNC 0 is a class consisting of quantum operations computed by constantdepth quantum ..."
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Abstract. We investigate a class QNC 0 (ADD) that is QNC 0 with gates for addition of two binary numbers, where QNC 0 is a class consisting of quantum operations computed by constantdepth quantum
Lower Bounds to the Size of ConstantDepth Propositional Proofs
, 1994
"... 1 LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives : and V ; W (both of unbounded arity). Then for every d 0 and n 2, there is a set T d n of depth d sequents of total size O(n 3+d ) which are refutable in LK by depth d + 1 proof of size exp ..."
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Cited by 57 (7 self)
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1 LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives : and V ; W (both of unbounded arity). Then for every d 0 and n 2, there is a set T d n of depth d sequents of total size O(n 3+d ) which are refutable in LK by depth d + 1 proof of size
Lower Bounds on Interactive Compressibility by ConstantDepth Circuits
, 2012
"... We formulate a new connection between instance compressibility [HN10]), where the compressor uses circuits from a class C, and correlation with circuits in C. We use this connection to prove the first lower bounds on general probabilistic multiround instance compression. We show that there is no pr ..."
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. We also consider the question of round separation, i.e., whether for each r � 1, there are functions which can be compressed better with r rounds of compression than with r − 1 rounds. We answer this question affirmatively for compression using constantdepth polynomialsize circuits. Finally, we
Results 1  10
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215,665