scholarly journals Rotation Based MSS/MCS Enumeration

10.29007/8btb ◽  
2020 ◽  
Author(s):  
Jaroslav Bendík ◽  
Ivana Cerna
Keyword(s):  
Time Limit ◽  
Satisfiability Problem ◽  
Experimental Comparison ◽  
Boolean Formula ◽  
Enumeration Algorithm ◽  
Complete Enumeration ◽  
Enumeration Algorithms

Given an unsatisfiable Boolean Formula F in CNF, i.e., a set of clauses, one is often interested in identifying Maximal Satisfiable Subsets (MSSes) of F or, equivalently, the complements of MSSes called Minimal Correction Subsets (MCSes). Since MSSes (MC- Ses) find applications in many domains, e.g. diagnosis, ontologies debugging, or axiom pinpointing, several MSS enumeration algorithms have been proposed. Unfortunately, finding even a single MSS is often very hard since it naturally subsumes repeatedly solving the satisfiability problem. Moreover, there can be up to exponentially many MSSes, thus their complete enumeration is often practically intractable. Therefore, the algorithms tend to identify as many MSSes as possible within a given time limit. In this work, we present a novel MSS enumeration algorithm called RIME. Compared to existing algorithms, RIME is much more frugal in the number of performed satisfiability checks which we witness via an experimental comparison. Moreover, RIME is several times faster than existing tools.

scholarly journals A Comprehensive Study of the Key Enumeration Problem

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 972 ◽  
Author(s):  
Ricardo Villanueva-Polanco
Keyword(s):  
Main Memory ◽  
Side Channel ◽  
Secret Key ◽  
Side Channel Attack ◽  
Enumeration Algorithm ◽  
Key Recovery ◽  
Recovery Algorithm ◽  
Enumeration Problem ◽  
Enumeration Algorithms ◽  
Recovery Problem

In this paper, we will study the key enumeration problem, which is connected to the key recovery problem posed in the cold boot attack setting. In this setting, an attacker with physical access to a computer may obtain noisy data of a cryptographic secret key of a cryptographic scheme from main memory via this data remanence attack. Therefore, the attacker would need a key-recovery algorithm to reconstruct the secret key from its noisy version. We will first describe this attack setting and then pose the problem of key recovery in a general way and establish a connection between the key recovery problem and the key enumeration problem. The latter problem has already been studied in the side-channel attack literature, where, for example, the attacker might procure scoring information for each byte of an Advanced Encryption Standard (AES) key from a side-channel attack and then want to efficiently enumerate and test a large number of complete 16-byte candidates until the correct key is found. After establishing such a connection between the key recovery problem and the key enumeration problem, we will present a comprehensive review of the most outstanding key enumeration algorithms to tackle the latter problem, for example, an optimal key enumeration algorithm (OKEA) and several nonoptimal key enumeration algorithms. Also, we will propose variants to some of them and make a comparison of them, highlighting their strengths and weaknesses.

FROM XSAT TO SAT BY EXHIBITING BOOLEAN FUNCTIONS

2009 ◽  
Vol 18 (05) ◽  
pp. 783-799
Author(s):  
RICHARD OSTROWSKI ◽  
LIONEL PARIS
Keyword(s):  
Graph Coloring ◽  
Boolean Functions ◽  
Structural Information ◽  
Conjunctive Normal Form ◽  
Satisfiability Problem ◽  
Boolean Formula ◽  
Truth Assignment ◽  
Coloring Problem ◽  
Graph Coloring Problem ◽  
Speed Up

Given a Boolean formula in conjunctive normal form (CNF), the Exact Satisfiability problem (XSAT), a variant of the Satisfiability problem (SAT), consists in finding an assignment to the variables such that each clause contains exactly one satisfied literal. Best algorithms to solve this problem run in [Formula: see text] ([Formula: see text] for X3SAT). Another possibility is to transform each clause in a set of equivalent clauses for the Satisfiability problem and to use modern and powerful solvers (zChaff, Berkmin, MiniSat, RSat etc.) to find such truth assignment. In this paper we introduce three new encodings from XSAT instances to SAT instances that lead to a lot of structural information (equivalency gates and and gates) which is naturally hidden in the pairwise transformation. Some solvers (lsat,march_dl,eqsatz) can take into account this kinds of structural information to make simplifications as pretreatment and speed-up the resolution. Then we show the interest of dealing with the XSAT formalism by introducing an encoding of binary CSP and graph coloring problem into XSAT instances. Preliminary results on real-world binary CSP and graph coloring problem show the importance of exhibiting equivalencies for the XSAT problem.

A New Algorithm for the Single Source Weber Problem with Limited Distances

2021 ◽  
Vol 55 (5) ◽  
pp. 1136-1150
Author(s):  
Giovanni Righini
Keyword(s):  
Time Complexity ◽  
Location Theory ◽  
Continuous Optimization ◽  
Intersection Point ◽  
Weber Problem ◽  
Single Source ◽  
Enumeration Algorithm ◽  
Worst Case ◽  
Enumeration Algorithms ◽  
Pass Through

The single source Weber problem with limited distances (SSWPLD) is a continuous optimization problem in location theory. The SSWPLD algorithms proposed so far are based on the enumeration of all regions of [Formula: see text] defined by a given set of n intersecting circumferences. Early algorithms require [Formula: see text] time for the enumeration, but they were recently shown to be incorrect in case of degenerate intersections, that is, when three or more circumferences pass through the same intersection point. This problem was fixed by a modified enumeration algorithm with complexity [Formula: see text], based on the construction of neighborhoods of degenerate intersection points. In this paper, it is shown that the complexity for correctly dealing with degenerate intersections can be reduced to [Formula: see text] so that existing enumeration algorithms can be fixed without increasing their [Formula: see text] time complexity, which is due to some preliminary computations unrelated to intersection degeneracy. Furthermore, a new algorithm for enumerating all regions to solve the SSWPLD is described: its worst-case time complexity is [Formula: see text]. The new algorithm also guarantees that the regions are enumerated only once.

A Polynomial Algorithm for Constructing a Large Bipartite Subgraph, with an Application to a Satisfiability Problem

1982 ◽  
Vol 34 (3) ◽  
pp. 519-524 ◽  
Author(s):  
Svatopluk Poljak ◽  
Daniel Turzík
Keyword(s):  
Connected Graph ◽  
Polynomial Algorithm ◽  
Short Proof ◽  
Satisfiability Problem ◽  
Boolean Formula ◽  
Complete Problem ◽  
Bipartite Subgraph ◽  
Np Complete ◽  
Image Position

Let G be a symmetric connected graph without loops. Denote by b(G) the maximum number of edges in a bipartite subgraph of G. Determination of b(G) is polynomial for planar graphs ([6], [8]); in general it is an NP-complete problem ([5]). Edwards in [1], [2] found some estimates of b(G) which give, in particular,for a connected graph G of n vertices and m edges, whereand ﹛x﹜ denotes the smallest integer ≧ x.We give an 0(V3) algorithm which for a given graph constructs a bipartite subgraph B with at least f(m, n) edges, yielding a short proof of Edwards’ result.Further, we consider similar methods for obtaining some estimates for a particular case of the satisfiability problem. Let Φ be a Boolean formula of variables x1, …, xn.

The Monotone Satisfiability Problem with Bounded Variable Appearances

2018 ◽  
Vol 29 (06) ◽  
pp. 979-993 ◽  
Author(s):  
Andreas Darmann ◽  
Janosch Döcker ◽  
Britta Dorn
Keyword(s):  
Computational Complexity ◽  
Satisfiability Problem ◽  
Boolean Formula ◽  
Incidence Graph ◽  
Complexity Status

The prominent Boolean formula satisfiability problem SAT is known to be [Formula: see text]-complete even for very restricted variants such as 3-SAT, Monotone 3-SAT, or Planar 3-SAT, or instances with bounded variable appearance. We settle the computational complexity status for two variants with bounded variable appearance: We show that Planar Monotone Sat — the variant of Monotone Sat in which the incidence graph is required to be planar — is [Formula: see text]-complete even if each clause consists of at most three distinct literals and each variable appears exactly three times, and that Monotone Sat is [Formula: see text]-complete even if each clause consists of three distinct literals and each variable appears exactly four times in the formula. The latter confirms a conjecture stated in scribe notes [7] of an MIT lecture by Eric Demaine. In addition, we provide hardness results with respect to bounded variable appearances for two variants of Planar Monotone Sat.

scholarly journals MAX-SAT Problem using Hybrid Harmony Search Algorithm

2018 ◽  
Vol 27 (4) ◽  
pp. 643-658 ◽  
Author(s):  
Iyad Abu Doush ◽  
Amal Lutfi Quran ◽  
Mohammed Azmi Al-Betar ◽  
Mohammed A. Awadallah
Keyword(s):  
Search Algorithm ◽  
Harmony Search ◽  
Harmony Search Algorithm ◽  
Satisfiability Problem ◽  
Boolean Formula ◽  
Stochastic Local Search ◽  
Boolean Variable ◽  
Sat Problem ◽  
Max Sat ◽  
The Impact

Abstract Maximum Satisfiability problem is an optimization variant of the Satisfiability problem (SAT) denoted as MAX-SAT. The aim of this problem is to find Boolean variable assignment that maximizes the number of satisfied clauses in the Boolean formula. In case the number of variables per clause is equal or greater than three, then this problem is considered NP-complete. Hence, many researchers have developed techniques to deal with MAX-SAT. In this paper, we investigate the impact of different hybrid versions of binary harmony search (HS) algorithm on solving MAX 3-SAT problem. Therefore, we propose two novel hybrid binary HS algorithms. The first hybridizes Flip heuristic with HS, and the second uses Tabu search combined with Flip heuristic. Furthermore, a distinguished feature of our proposed approaches is using an objective function that is updated dynamically based on the stepwise adaptation of weights (SAW) mechanism to evaluate the MAX-SAT solution using the proposed hybrid versions. The performance of the proposed approaches is evaluated over standard MAX-SAT benchmarks, and the results are compared with six evolutionary algorithms and three stochastic local search algorithms. The obtained results are competitive and show that the proposed novel approaches are effective.

scholarly journals Formal Development of Distributed Enumeration Algorithms By Refinement-Based Techniques

10.29007/8n75 ◽  
2018 ◽  
Author(s):  
Maha Boussabbeh ◽  
Mohamed Tounsi ◽  
Ahmed Hadj Kacem ◽  
Mohamed Mosbah
Keyword(s):  
Distributed Algorithms ◽  
Main Idea ◽  
Top Down ◽  
Enumeration Algorithm ◽  
Modelling Language ◽  
Formal Development ◽  
Distributed Computations ◽  
Enumeration Problem ◽  
Enumeration Algorithms ◽  
Incremental Process

The enumeration problem addresses a collection of important algorithmic issues related to distributed computations. Among existing solutions, we are interested on the seminal algorithm of Mazurkiewicz, based on local computations. Our paper contributes to the design of a correct-by-construction enumeration algorithm. The main idea relies upon the development of the problem following a top/down approachthat can be supported by an incremental process controlled by the refinement of models. Event-B modelling language is supporting our methodological. Our main objective is to provide a verified component for distributed enumeration inorder to be used and extended for solving other problems of distributed algorithms.

scholarly journals Behaviour examples for synthesizing automaton models by temporal formulas

2021 ◽  
Vol 34 (01) ◽  
pp. 61-73
Author(s):  
Dmitry V. Pashchenko ◽  
Alexey I. Martyshkin ◽  
Dmitry A. Trokoz ◽  
Tatyana Yu. Pashchenko ◽  
Mikhail Yu. Babich ◽  
...  
Keyword(s):  
Experimental Study ◽  
Experimental Results ◽  
Satisfiability Problem ◽  
Boolean Formula ◽  
New Methods ◽  
Boolean Formulas ◽  
Basic Approaches

The paper deals with researching and developing the methods that make it possible to account behaviour examples when synthesizing automaton models by temporal formulas. Definitions of the terms and concepts used in work are given; the problem of synthesizing automaton systems according to the specification in the form of temporal formulas and behaviour examples is formulated; a promising algorithm for reducing the problem of synthesizing automaton systems to the Boolean formula satisfiability problem is described; an analysis of the domain and other approaches is carried out. New methods of taking into account behaviour examples in the synthesis of automaton systems according to a specification given in the form of temporal formulas are proposed. Algorithms for constructing graphs of scripts and methods for dividing graphs into clusters are described; they are designed to increase the efficiency of representing behaviour examples used for coding the behaviour examples in the form of Boolean formulas. An experimental study of the proposed methods of accounting for behaviour examples and basic approaches to the presentation of behaviour examples is carried out. The experimental results showed the superiority of the newly developed methods regarding the presentation of scripts in the form of temporal formulas. In summary, the main conclusions of the work carried out are presented.

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