Results 11  20
of
80
A Design Methodology for SelfTimed Systems
, 1981
"... This thesis presents a design methodology for selftimed systems which will be extremely attractive for implementing systems in VLSI. Selftimed systems are characterized by the absence of a timing reference to which all operations are synchronized. Currently most systems are implemented using a syn ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
This thesis presents a design methodology for selftimed systems which will be extremely attractive for implementing systems in VLSI. Selftimed systems are characterized by the absence of a timing reference to which all operations are synchronized. Currently most systems are implemented using a synchronous design methodology where all operations are synchronized to a global clock. However, this approach will not be attractive in the future for implementing systems in VLSI due to the high communication costs in VLSI and the prohibitive task of managing timing constraints global to a VLSI integrated circuit.
Abstract interpretation using typed decision graphs
 Science of Computer Programming
, 1998
"... Abstract. This article presents a way of implementing abstract interpretations that can be very efficient. The improvement lies in the use of a symbolic representation of boolean functions called Typed Decision Graphs (TDGs), a refinement of Binary Decision Diagrams. A general procedure for using th ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
Abstract. This article presents a way of implementing abstract interpretations that can be very efficient. The improvement lies in the use of a symbolic representation of boolean functions called Typed Decision Graphs (TDGs), a refinement of Binary Decision Diagrams. A general procedure for using this representation in abstract interpretation is given; we examine in particular the possibility of encoding higher order functions into TDGs. Moreover, this representation is used to design a widening operator based on the size of the objects represented, so that abstract interpretations will not fail due to insufficient memory. This approach is illustrated on strictness analysis of higherorder functions, showing a great increase in efficiency. 1
Some Problems Involving RazborovSmolensky Polynomials
, 1991
"... Several recent results in circuit complexity theory have used a representation of Boolean functions by polynomials over finite fields. Our current inability to extend these results to superficially similar situations may be related to properties of these polynomials which do not extend to polyno ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
Several recent results in circuit complexity theory have used a representation of Boolean functions by polynomials over finite fields. Our current inability to extend these results to superficially similar situations may be related to properties of these polynomials which do not extend to polynomials over general finite rings or finite abelian groups. Here we pose a number of conjectures on the behavior of such polynomials over rings and groups, and present some partial results toward proving them. 1. Introduction 1.1. Polynomials and Circuit Complexity The representation of Boolean functions as polynomials over the finite field Z 2 = f0; 1g dates back to early work in switching theory [?]. A formal language L can be identified with the family of functions f i : Z i 2 ! Z 2 , where f i (x 1 ; : : : ; x i ) = 1 iff x 1 : : : x i 2 L. Each of these functions can be written as a polynomial in the variables x 1 ; : : : ; x n . We can consider algebraic formulas or circuits with...
Factored EdgeValued Binary Decision Diagrams and their Application to Matrix Representation and Manipulation
 FORMAL METHODS IN SYSTEM DESIGN
, 1994
"... Factored EdgeValued Binary Decision Diagrams form an extension to EdgeValued Binary Decision Diagrams. By associating both an additive and a multiplicative weight with the edges, FEVBDDs can be used to represent a wider range of functions concisely. As a result, the computational complexity for ce ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
Factored EdgeValued Binary Decision Diagrams form an extension to EdgeValued Binary Decision Diagrams. By associating both an additive and a multiplicative weight with the edges, FEVBDDs can be used to represent a wider range of functions concisely. As a result, the computational complexity for certain operations can be significantly reduced compared to EVBDDs. Additionally, the introduction of multiplicative edge weights allows us to directly represent the socalled complement edges which are used in OBDDs, thus providing a one to one mapping of all OBDDs to FEVBDDs. Applications such as integer linear programming and logic verification that have been proposed for EVBDDs also benefit from the extension. We present a complete matrix package based on FEVBDDs and apply the package to the problem of solving the ChapmanKolmogorov equations.
Using the Minimum Description Length Principle to Infer Reduced Ordered Decision Graphs
 Machine Learning
, 1996
"... . We propose an algorithm for the inference of decision graphs from a set of labeled instances. In particular, we propose to infer decision graphs where the variables can only be tested in accordance with a given order and no redundant nodes exist. This type of graphs, reduced ordered decision graph ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
. We propose an algorithm for the inference of decision graphs from a set of labeled instances. In particular, we propose to infer decision graphs where the variables can only be tested in accordance with a given order and no redundant nodes exist. This type of graphs, reduced ordered decision graphs, can be used as canonical representations of Boolean functions and can be manipulated using algorithms developed for that purpose. This work proposes a local optimization algorithm that generates compact decision graphs by performing local changes in an existing graph until a minimum is reached. The algorithm uses Rissanen's minimum description length principle to control the tradeoff between accuracy in the training set and complexity of the description. Techniques for the selection of the initial decision graph and for the selection of an appropriate ordering of the variables are also presented. Experimental results obtained using this algorithm in two sets of examples are presented and ...
An Extended Theory of Boolean Normal Forms
 in: Proceedings of the 6th Annual Hawaii International Conference on Statistics, Mathematics and Related Fields
, 2007
"... Normal forms of Boolean functions allow to check whether two given Boolean expressions describe the same Boolean function. The disjunctive normal form (DNF) as well as the conjunctive normal form (CNF) are widely used. Sometimes an algebraic normal form is taken into account in order to compare or t ..."
Abstract

Cited by 11 (11 self)
 Add to MetaCart
Normal forms of Boolean functions allow to check whether two given Boolean expressions describe the same Boolean function. The disjunctive normal form (DNF) as well as the conjunctive normal form (CNF) are widely used. Sometimes an algebraic normal form is taken into account in order to compare or to evaluate given Boolean functions. The basic property of each normal form is the unique representation of the given Boolean function. The aim of this paper is to study whether there are other normal forms of Boolean functions which allow a more detailed exploration of properties of Boolean Functions. In order to do this we extend the theory of Boolean normal forms in several directions. 1
Boolean Constraints in SICStus Prolog
, 1994
"... This report documents the implementation of a Boolean constraint solver and its integration with a Prolog engine. The solver comprises builtin predicates for checking consistency and entailment of a new constraint w.r.t. accumulated constraints and for generating particular solutions to a set of co ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
This report documents the implementation of a Boolean constraint solver and its integration with a Prolog engine. The solver comprises builtin predicates for checking consistency and entailment of a new constraint w.r.t. accumulated constraints and for generating particular solutions to a set of constraints, and extensions to the Prolog toplevel for displaying answer constraints. Boolean unification was chosen as the strategy for the consistency check. Boolean unification fits well with the Prolog execution model, and allows the accumulated constraints to be associated in a natural way with the variables being eliminated. The answer constraints are computed by existentially quantifying in the accumulated set of constraints all variables not occurring in the user query. The simplified set of constraints constitutes the answer constraints. Boolean formulas are internally represented as DAGs. Details are provided on this representation and the support for it provided by the Prolog Engin...
A Probabilistic Logic For The Development Of SafetyCritical, Interactive Systems
 International Journal Of ManMachine Studies
, 1993
"... This paper starts from the premise that the human contribution to risk must be assessed during the development of safetycritical systems. In contrast to previous approaches, discrete numerical values are rejected as means of quantifying the probability of operator `error' for many different users o ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
This paper starts from the premise that the human contribution to risk must be assessed during the development of safetycritical systems. In contrast to previous approaches, discrete numerical values are rejected as means of quantifying the probability of operator `error' for many different users of many different systems. Numerical probabilities are used to rank the importance that designers attach to particular system failures. Adequate development resources must be allocated so that operators will resolve and not exacerbate high priority failures. In order to do this, human factors and systems engineers must be provided with notations that can represent risk assessments. Many techniques that are in widespread use, such as faulttree analysis, provide inadequate support for the development of interactive systems. They do not capture the temporal properties that can determine the quality of interaction between operators and stochastic application processes. It is argued that probabil...
Computational Complexity
, 2004
"... The strive for efficiency is ancient and universal, as time is always short for humans. Computational Complexity is a mathematical study of the what can be achieved when time (and other resources) are scarce. In this ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
The strive for efficiency is ancient and universal, as time is always short for humans. Computational Complexity is a mathematical study of the what can be achieved when time (and other resources) are scarce. In this
Stochastic Switching Circuit Synthesis
"... In his 1938 Master’s Thesis, Shannon demonstrated that any Boolean function can be realized by a switching relay circuit, leading to the development of deterministic digital logic. Here, we replace each classical switch with a probabilistic switch (pswitch). We present algorithms for synthesizing ci ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
In his 1938 Master’s Thesis, Shannon demonstrated that any Boolean function can be realized by a switching relay circuit, leading to the development of deterministic digital logic. Here, we replace each classical switch with a probabilistic switch (pswitch). We present algorithms for synthesizing circuits closed with a desired probability, including an algorithm that generates optimal size circuits for any binary fraction. We also introduce a new duality property for seriesparallel stochastic switching circuits. Finally, we construct a universal probability generator which maps deterministic inputs to arbitrary probabilistic outputs. Potential applications exist in the analysis and design of stochastic networks in biology and engineering. I. INTRODUCTION. Claude Shannon, in his 1938 Master’s Thesis, discovered a systematic synthesis procedure to realize a given Boolean function using deterministic switches [Sha38]. This classical contribution led to the development of modern digital logic design and is at the foundation of our ability to design and manufacture digital circuits with millions of transistors.