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On the robustness of random Boolean formulae

2010
*
Journal of Physics, Conference Series
*

Random

doi:10.1088/1742-6596/233/1/012015
fatcat:flz53sg3mbfu7mxkqbljemayu4
*Boolean**formulae*, generated by a growth process*of*noisy logical gates are analyzed using the generating functional methodology*of*statistical physics. ... We study the type*of*functions generated for different input distributions, their robustness for a given level*of*gate error and its dependence on the*formulae*depth and complexity and the gates used. ... The DNF or its dual CNF (conjunctive normal form) is a depth-2*formula*with AND*and**OR*gates used as internal nodes and with the input*Boolean*variables and their negations distributed on the leaves. ...##
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Noisy random Boolean formulae: A statistical physics perspective

2010
*
Physical Review E
*

A growth model that gives rise to

doi:10.1103/physreve.82.041112
pmid:21230243
fatcat:xrhkddzvgfewpjj5mvxshbajwi
*typical*random*Boolean*functions is mapped onto a layered Ising spin system, which facilitates the study*of*their ability to represent arbitrary*formulae*with a given ...*Typical**properties**of*computing circuits composed*of*noisy logical gates are studied using the statistical physics methodology. ... This method was used to investigate*typical**properties**of*random*Boolean**AND*/*OR**formulas*͓15-17͔ and obtain bounds on the probability P͑f͒*of*a random*formula*to compute a given*Boolean*function f; they ...##
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Complexity and Probability of Some Boolean Formulas

1998
*
Combinatorics, probability & computing
*

For any

doi:10.1017/s0963548398003630
fatcat:jk4qvoptxrctvdahcec6bo7p5e
*Boolean*function f let L(f) be its*formula*size complexity in the basis f^ 1g. ... The number B(n `)*of*distinct*Boolean*functions*of*n variables expressible by a n*AND*/*OR**formula**of*size at most`is estimated in 9]. ... A di erent model*of*random*Boolean**formulas*based on the uniform distribution on all*AND*/*OR**formulas**of*size tending to in nity w as investigated in 3]. ...##
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On the learnability of Boolean formulae

1987
*
Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87
*

T f is a rooted directed tree with variables as leaves, internal nodes labeled with

doi:10.1145/28395.28426
dblp:conf/stoc/KearnsLPV87
fatcat:q7pi5rwh2vhcvmmljaklerwcay
*AND*",*OR*", and NOT", and edges directed away from the root. ... The results*of*this paper fall into three categories: closure*properties**of*learnable classes, negative results, and distribution-speci c positive results. The closure*properties*are*of*two kinds. ...##
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On Tractability of Disjoint AND-Decomposition of Boolean Formulas
[chapter]

2015
*
Lecture Notes in Computer Science
*

Disjoint AND-decomposition

doi:10.1007/978-3-662-46823-4_8
fatcat:boaglm6gpfgwhauaalbo6hgdom
*of*a*boolean**formula*means its representation as a conjunction*of*two (or several)*formulas*having disjoint sets*of*variables. ... We show that deciding AND-decomposability is intractable in general for*boolean**formulas*given in CNF or DNF and prove tractability*of*computing AND-decompositions*of**boolean**formulas*given in positive ... The obtained*formulas*define*some*partition*of*var (ϕ) and the fact below (which follows from a*property**of*a*large*class*of*logical calculi shown in [12] ) says that this variable partition is unique ...##
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A self-adaptive multi-engine solver for quantified Boolean formulas

2008
*
Constraints
*

In this paper we study the problem

doi:10.1007/s10601-008-9051-2
fatcat:zbrs2atvpvakzgabktmfzj2plq
*of*engineering a robust solver for quantified*Boolean**formulas*(QBFs), i.e., a tool that can efficiently solve*formulas*across different problem domains without the need ... with previously uncharted*formulas*and competitors. ... Acknowledgements We wish to thank the Italian Ministry*of*University and Research for its financial support. ...##
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Learning Heuristics for Quantified Boolean Formulas through Deep Reinforcement Learning
[article]

2019
*
arXiv
*
pre-print

We demonstrate how to learn efficient heuristics for automated reasoning algorithms for quantified

arXiv:1807.08058v3
fatcat:fcfcgk4yfngbfiov3irbv53luq
*Boolean**formulas*through deep reinforcement learning. ... We focus on a backtracking search algorithm, which can already solve*formulas**of*impressive size - up to hundreds*of*thousands*of*variables. ... Propositional*Boolean*logic allows us to use the constants 0 (false) and 1 (true), variables, and the standard*Boolean*operators like ∧ ("*and*"), ∨ ("*or*"), and ¬ ("not"). ...##
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Boolean Formulas for the Static Identification of Injection Attacks in Java
[chapter]

2015
*
Lecture Notes in Computer Science
*

The analysis works by translating the program into

doi:10.1007/978-3-662-48899-7_10
fatcat:lusfgogeenhqvjiv7w5hdp4p2y
*Boolean**formulas*that model all possible flows. We implemented it within the Julia analyzer for Java and Android. ... Julia found injection security vulnerabilities in the Internet banking service and in the customer relationship management*of*a*large*Italian bank. ... Julia represents*Boolean**formulas*via BDDs (binary decision diagrams). ...##
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Betting Boolean-style: a framework for trading in securities based on logical formulas

2005
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Decision Support Systems
*

A compound securities market allows agents to place bets on arbitrary

doi:10.1016/j.dss.2004.08.010
fatcat:hdam4aigi5czflcyink742huyq
*boolean*combinations*of*events, enabling them to more closely achieve their optimal risk exposure, and enabling the market as a whole ... We develop and motivate the concept*of*a compound securities market, presenting the framework through a series*of*formal definitions and examples. ... To show co-NP-completeness we reduce the NP-complete problem*of**Boolean**formula*satisfiability to the nonexistence*of*a matching. Fix a*formula*φ. ...##
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Betting boolean-style: a framework for trading in securities based on logical formulas

2003
*
Proceedings of the 4th ACM conference on Electronic commerce - EC '03
*

A compound securities market allows agents to place bets on arbitrary

doi:10.1145/779928.779946
dblp:conf/sigecom/FortnowKPW03
fatcat:sqevn4lamnctblt5nl37jzoff4
*boolean*combinations*of*events, enabling them to more closely achieve their optimal risk exposure, and enabling the market as a whole ... We develop and motivate the concept*of*a compound securities market, presenting the framework through a series*of*formal definitions and examples. ... To show co-NP-completeness we reduce the NP-complete problem*of**Boolean**formula*satisfiability to the nonexistence*of*a matching. Fix a*formula*φ. ...##
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No ifs, ands, or buts

2007
*
Proceedings of the 22nd annual ACM SIGPLAN conference on Object oriented programming systems and applications - OOPSLA '07
*

They give program logic the clarity

doi:10.1145/1297027.1297075
dblp:conf/oopsla/Edwards07
fatcat:itzxwa5ymrbkxetglhro77wsw4
*of*truth tables, and support high-level direct manipulation*of*that logic, avoiding much*of*the mental computation demanded by conventional conditionals. ... They unify the full range*of*conditional constructs, from if statements through pattern matching to polymorphic predicate dispatch. ... To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission*and*/*or*a fee. situations, and they establish much*of*a program's structure. ...##
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No ifs, ands, or buts

2007
*
SIGPLAN notices
*

They give program logic the clarity

doi:10.1145/1297105.1297075
fatcat:sx2zzwwmanbddohbdtgczvupam
*of*truth tables, and support high-level direct manipulation*of*that logic, avoiding much*of*the mental computation demanded by conventional conditionals. ... They unify the full range*of*conditional constructs, from if statements through pattern matching to polymorphic predicate dispatch. ... To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission*and*/*or*a fee. situations, and they establish much*of*a program's structure. ...##
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Subcritical pattern languages for and/or trees

2008
*
Discrete Mathematics & Theoretical Computer Science
*

International audience Let $P_k(f)$ denote the density

doi:10.46298/dmtcs.3582
fatcat:sf2agn4lsbd6vniotd2rhp37mm
*of**and*/*or*trees defining a*boolean*function $f$ within the set*of**and*/*or*trees with fixed number*of*variables $k$. ... We prove that there exists constant $B_f$ such that $P_k(f) \sim B_f \cdot k^{-L(f)-1}$ when $k \to \infty$, where $L(f)$ denote the complexity*of*$f$ (i.e. the size*of*a minimal*and*/*or*tree defining $ ... Since every*and*/*or*tree using at most variables {x 1 , . . . , x k } defines*some**boolean*function f : {0, 1} k → {0, 1}, the uniform probability distribution on the*and*/*or*trees*of*size n induces*some*...##
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And/or trees: A local limit point of view
[article]

2017
*
arXiv
*
pre-print

An

arXiv:1510.06691v2
fatcat:zvlr7quth5etthlppgpa6hkaza
*and*/*or*tree is a*Boolean*expression represented in (one*of*) its tree shapes. ... We present here a new and universal approach for the study*of*random*and*/*or*trees, unifying in one framework many different models, including*some*novel ones not yet understood in the literature. ... binary*and*/*or*trees*of*size n, respectively. ...##
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A Lossless Fuzzy Binary AND/OR Compressor
[article]

2009
*
arXiv
*
pre-print

Data decompression/specific data reconstruction initiates an

arXiv:0910.2066v2
fatcat:osxvxncikbgsvbecu7v4yyphsq
*AND*/*OR*pattern match technique in respect*of*fuzzy quantum indicators in the binary function field. ... a (1/2 upper +1/2 lower)-bit noise frequency parallel to its counterpart signal comprised*of**AND*/*ORed*-bit polarity orientation, ready for an identical data decompression. ... Axelsson from the Faculty*of*Department*of*Software Engineering and Computer Science, Blekinge Institute*of*Technology, Sweden (2009). ...
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