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On the robustness of random Boolean formulae

Alexander Mozeika, David Saad, Jack Raymond
2010 Journal of Physics, Conference Series  
Random 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.  ... 
doi:10.1088/1742-6596/233/1/012015 fatcat:flz53sg3mbfu7mxkqbljemayu4

Noisy random Boolean formulae: A statistical physics perspective

Alexander Mozeika, David Saad, Jack Raymond
2010 Physical Review E  
A growth model that gives rise to 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  ... 
doi:10.1103/physreve.82.041112 pmid:21230243 fatcat:xrhkddzvgfewpjj5mvxshbajwi

Complexity and Probability of Some Boolean Formulas

PETR SAVICKÝ
1998 Combinatorics, probability & computing  
For any 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].  ... 
doi:10.1017/s0963548398003630 fatcat:jk4qvoptxrctvdahcec6bo7p5e

On the learnability of Boolean formulae

M. Kearns, M. Li, L. Pitt, L. Valiant
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 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.  ... 
doi:10.1145/28395.28426 dblp:conf/stoc/KearnsLPV87 fatcat:q7pi5rwh2vhcvmmljaklerwcay

On Tractability of Disjoint AND-Decomposition of Boolean Formulas [chapter]

Pavel Emelyanov, Denis Ponomaryov
2015 Lecture Notes in Computer Science  
Disjoint AND-decomposition 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  ... 
doi:10.1007/978-3-662-46823-4_8 fatcat:boaglm6gpfgwhauaalbo6hgdom

A self-adaptive multi-engine solver for quantified Boolean formulas

Luca Pulina, Armando Tacchella
2008 Constraints  
In this paper we study the problem 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.  ... 
doi:10.1007/s10601-008-9051-2 fatcat:zbrs2atvpvakzgabktmfzj2plq

Learning Heuristics for Quantified Boolean Formulas through Deep Reinforcement Learning [article]

Gil Lederman and Markus N. Rabe and Edward A. Lee and Sanjit A. Seshia
2019 arXiv   pre-print
We demonstrate how to learn efficient heuristics for automated reasoning algorithms for quantified 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").  ... 
arXiv:1807.08058v3 fatcat:fcfcgk4yfngbfiov3irbv53luq

Boolean Formulas for the Static Identification of Injection Attacks in Java [chapter]

Michael D. Ernst, Alberto Lovato, Damiano Macedonio, Ciprian Spiridon, Fausto Spoto
2015 Lecture Notes in Computer Science  
The analysis works by translating the program into 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).  ... 
doi:10.1007/978-3-662-48899-7_10 fatcat:lusfgogeenhqvjiv7w5hdp4p2y

Betting Boolean-style: a framework for trading in securities based on logical formulas

Lance Fortnow, Joe Kilian, David M. Pennock, Michael P. Wellman
2005 Decision Support Systems  
A compound securities market allows agents to place bets on arbitrary 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.  ... 
doi:10.1016/j.dss.2004.08.010 fatcat:hdam4aigi5czflcyink742huyq

Betting boolean-style: a framework for trading in securities based on logical formulas

Lance Fortnow, Joe Kilian, David M. Pennock, Michael P. Wellman
2003 Proceedings of the 4th ACM conference on Electronic commerce - EC '03  
A compound securities market allows agents to place bets on arbitrary 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.  ... 
doi:10.1145/779928.779946 dblp:conf/sigecom/FortnowKPW03 fatcat:sqevn4lamnctblt5nl37jzoff4

No ifs, ands, or buts

Jonathan Edwards
2007 Proceedings of the 22nd annual ACM SIGPLAN conference on Object oriented programming systems and applications - OOPSLA '07  
They give program logic the clarity 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.  ... 
doi:10.1145/1297027.1297075 dblp:conf/oopsla/Edwards07 fatcat:itzxwa5ymrbkxetglhro77wsw4

No ifs, ands, or buts

Jonathan Edwards
2007 SIGPLAN notices  
They give program logic the clarity 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.  ... 
doi:10.1145/1297105.1297075 fatcat:sx2zzwwmanbddohbdtgczvupam

Subcritical pattern languages for and/or trees

Jakub Kozik
2008 Discrete Mathematics & Theoretical Computer Science  
International audience Let $P_k(f)$ denote the density 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  ... 
doi:10.46298/dmtcs.3582 fatcat:sf2agn4lsbd6vniotd2rhp37mm

And/or trees: A local limit point of view [article]

Nicolas Broutin, Cécile Mailler
2017 arXiv   pre-print
An 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.  ... 
arXiv:1510.06691v2 fatcat:zvlr7quth5etthlppgpa6hkaza

A Lossless Fuzzy Binary AND/OR Compressor [article]

Philip B. Alipour
2009 arXiv   pre-print
Data decompression/specific data reconstruction initiates an 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).  ... 
arXiv:0910.2066v2 fatcat:osxvxncikbgsvbecu7v4yyphsq
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