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Two classes of Boolean functions for dependency analysis

Tania Armstrong, Kim Marriott, Peter Schachte, Harald Søndergaard
1998 Science of Computer Programming  
We identify two classes of Boolean functions that have been used: positive and definite functions, and we systematically investigate these classes and their efficient implementation for dependency analyses  ...  Examples include groundness analysis, arguably the most important analysis for logic programs, finiteness analysis and functional dependency analysis for databases.  ...  Our contributions are twofold: First we provide simple syntactic characterizations for positive and definite functions and study their algebraic properties.  ... 
doi:10.1016/s0167-6423(96)00039-1 fatcat:myvly7jm7bbytb57zurobdmz4y

Boolean Functions for Finite-Tree Dependencies [chapter]

Roberto Bagnara, Enea Zaffanella, Roberta Gori, Patricia M. Hill
2001 Lecture Notes in Computer Science  
Here we present a domain of Boolean functions, called finite-tree dependencies that precisely captures how the finiteness of some variables influences the finiteness of other variables.  ...  For instance, many of the built-in and library predicates are ill-defined for such trees and need to be supplemented by run-time checks whose cost may be significant.  ...  Therefore, in this paper we have introduced a domain of Boolean functions Bfun for finite-tree dependencies which, when coupled to the domain H × P , can enhance its expressive power.  ... 
doi:10.1007/3-540-45653-8_40 fatcat:6qussizz7fflpnxths536d42ia

Algebraic Polynomial-based Synthesis for Abstract Boolean Network Analysis

Peter Backeman, Christoph M. Wintersteiger, Boyan Yordanov, Sara-Jane Dunn
2016 Conference on Automated Deduction  
We present an investigation of restrictions to templates over Boolean functions of polynomial shape, based on their algebraic normal form.  ...  This method is then implemented using an SMT-solver (Z3) and illustrated on a biological problem, the goal of which is to synthesise (Boolean) gene regulatory networks that capture specifications derived  ...  An algebraic polynomial is conveniently described as a subset of the ANF monomials in its representation, and it represents a set of Boolean functions (those representable by concrete choices of values  ... 
dblp:conf/cade/BackemanWYD16 fatcat:hgxyjsmn4jbobdxgk4r5g6kk5m

S-box, SET, Match: A Toolbox for S-box Analysis [chapter]

Stjepan Picek, Lejla Batina, Domagoj Jakobović, Barış Ege, Marin Golub
2014 Lecture Notes in Computer Science  
In this paper we present a tool for the evaluation of Boolean functions and S-boxes suitable for cryptography.  ...  Boolean functions and substitution boxes (S-boxes) represent the only nonlinear part in many algorithms and therefore play the crucial role in their security.  ...  This work was supported in part by the Technology Foundation STW (project 12624 -SIDES), The Netherlands Organization for Scientific Research NWO (project ProFIL 628.001.007) and the ICT COST action IC1204  ... 
doi:10.1007/978-3-662-43826-8_10 fatcat:npa7oqi2gfakvop6z6gwrhduge

Analysis of combinational networks with mathematics

Dejan Tosic, Slobodan Simic
2005 Publikacija Elektrotehnickog fakulteta - serija matematika  
The symbolic analysis addressed in this work can serve as a basis of efficient programs for variety of logic design tasks, including logic simulation, fault simulation, test generation, and symbolic verification  ...  A novel program is presented to carry out the symbolic analysis, and to derive closed-form formulas for the response of combinational networks, for excitations specified by symbols or symbolic expressions  ...  CONCLUSION Basic concepts of symbolic analysis and Boolean algebra are reviewed.  ... 
doi:10.2298/petf0516098t fatcat:p6cexp5eana2naknzxqyo4ys3y

Steady state analysis of Boolean molecular network models via model reduction and computational algebra

Alan Veliz-Cuba, Boris Aguilar, Franziska Hinkelmann, Reinhard Laubenbacher
2014 BMC Bioinformatics  
Since the size of the state space of a Boolean model with n nodes is 2 n , this approach becomes unfeasible for larger models, those with more than approximately 30 variables, depending on the computational  ...  The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential.  ...  The idea is to represent the Boolean functions as a directed graph that efficiently encodes the functions by allowing fast evaluation.  ... 
doi:10.1186/1471-2105-15-221 pmid:24965213 pmcid:PMC4230806 fatcat:c6n667vqyrelld6sixldwgegqq

Algebraic Side-Channel Analysis in the Presence of Errors [chapter]

Yossef Oren, Mario Kirschbaum, Thomas Popp, Avishai Wool
2010 Lecture Notes in Computer Science  
We call our new attack methodology Tolerant Algebraic Side-Channel Analysis (TASCA). We show practical attacks on two real ciphers: Keeloq and AES.  ...  Recently it was suggested by [18] to use algebraic methods for the single-trace scenario, converting the key recovery problem into a Boolean satisfiability (SAT) problem, then using a SAT solver.  ...  The authors wish to thank the anonymous reviewers for their encouraging and insightful comments.  ... 
doi:10.1007/978-3-642-15031-9_29 fatcat:ysterkscqzd4lfh5wyby3wkazu

What Is Boolean Valued Analysis? [article]

S. S. Kutateladze
2009 arXiv   pre-print
This is a brief overview of the basic techniques of Boolean valued analysis.  ...  The technique of Boolean valued analysis demonstrates its efficiency in studying Banach spaces and algebras as well as lattice-normed spaces and modules.  ...  Many delicate properties of the objects inside Î (B) depend essentially on the structure of the initial Boolean algebra B.  ... 
arXiv:math/0610195v4 fatcat:igyev54ysvh2la7a376ve7nnsi

Symbolic analysis of bounded Petri nets

E. Pastor, J. Cortadella, O. Roig
2001 IEEE transactions on computers  
The structure and behavior of the Petri net is symbolically modeled by using Boolean functions, thus reducing reasoning about Petri nets to Boolean calculation.  ...  By using this symbolic framework, properties requiring an exhaustive analysis of the reachability graph can be efficiently verified.  ...  Theorem 1 (Stone's Representation Theorem). Every finite Boolean algebra is isomorphic to the Boolean algebra of subsets of some finite set S.  ... 
doi:10.1109/12.926158 fatcat:ihxqhffkx5allbonzdfrin6meq

Relation-algebraic analysis of Petri nets with RELVIEW [chapter]

Rudolf Berghammer, Burghard Karger, Christiane Ulke
1996 Lecture Notes in Computer Science  
We present a method for specifying and implementing algorithms for the analysis of Petri nets. It is formally grounded in relational algebra.  ...  Its simpficity and efficiency is illustrated in many examples.  ...  Efficient tests for Boolean matrices to be functional resp. injective inspect row by row resp. column by column, i.e., need only two nested loops.  ... 
doi:10.1007/3-540-61042-1_38 fatcat:sa26y3swyfbibhu2ullvtixahm

On Verifying Complex Properties using Symbolic Shape Analysis [article]

Thomas Wies, Viktor Kuncak, Karen Zee, Andreas Podelski, Martin Rinard
2006 arXiv   pre-print
We describe Bohne, a new analysis for verifying data structures.  ...  During the analysis, Bohne infers loop invariants in the form of disjunctions of universally quantified Boolean combinations of formulas.  ...  These partial orders induce Boolean algebra structures. We denote by ⊓, ⊔ and · the meet, join and complement operations of these Boolean algebras.  ... 
arXiv:cs/0609104v1 fatcat:fvo3jony5ja23fecutl6s5otzu

What is Boolean valued analysis?

S. S. Kutateladze
2007 Siberian Advances in Mathematics  
This is a brief overview of the basic techniques of Boolean valued analysis.  ...  Gutman for his numerous subtle improvements of the preprint of this talk in Russian.  ...  ACKNOWLEDGMENTS This article is an expanded version of a talk at Ta ˘ımanov's seminar on geometry, topology, and their applications in the Sobolev Institute of Mathematics on September 25, 2006.  ... 
doi:10.3103/s1055134407020022 fatcat:iwzlv72xobaxtc3tezm4jk4bxi

Symbolic pointer analysis revisited

Jianwen Zhu, Silvian Calman
2004 Proceedings of the ACM SIGPLAN 2004 conference on Programming language design and implementation - PLDI '04  
analysis, and results for context-sensitive analysis are only preliminary.  ...  In this paper, we refine the concept of symbolic transfer function proposed earlier and establish a common framework for both context-insensitive and context-sensitive pointer analysis.  ...  Since in our representation, a set of memory blocks can be represented as a Boolean function, the image computation can be formulated as Boolean function manipulation, which in turn can be efficiently  ... 
doi:10.1145/996841.996860 dblp:conf/pldi/ZhuC04 fatcat:bq4a6b6v7zaaja2ii6j2is3tia

Symbolic pointer analysis revisited

Jianwen Zhu, Silvian Calman
2004 SIGPLAN notices  
analysis, and results for context-sensitive analysis are only preliminary.  ...  In this paper, we refine the concept of symbolic transfer function proposed earlier and establish a common framework for both context-insensitive and context-sensitive pointer analysis.  ...  Since in our representation, a set of memory blocks can be represented as a Boolean function, the image computation can be formulated as Boolean function manipulation, which in turn can be efficiently  ... 
doi:10.1145/996893.996860 fatcat:z62gjno7izagrd7ssarsoll2de

Implicit structural analysis of multimode DAE systems

Benoît Caillaud, Mathias Malandain, Joan Thibault
2020 Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control  
A structural analysis algorithm for mDAE systems is presented, based on an implicit representation of the varying structure of an mDAE. It generalizes J.  ...  Pryce's structural analysis method to the multimode case and uses Binary Decision Diagrams (BDD) to represent the mode-dependent structure of an mDAE.  ...  Pryce's Σ-method), and compute a conditional dependency graph yielding all necessary information for efficient simulation code generation.  ... 
doi:10.1145/3365365.3382201 dblp:conf/hybrid/CaillaudMT20 fatcat:e3hlnynztjghhaydecw4pvufdm
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