scholarly journals The Model Counting Competition 2020

2021 ◽  
Vol 26 (1) ◽  
pp. 1-26
Author(s):  
Johannes K. Fichte ◽  
Markus Hecher ◽  
Florim Hamiti
Keyword(s):  
Practical Problem ◽  
Probabilistic Reasoning ◽  
Modern Society ◽  
Boolean Formula ◽  
Counting Problem ◽  
The Past ◽  
Boolean Formulas ◽  
Model Counting ◽  
Weighted Model ◽  
New Applications

Many computational problems in modern society account to probabilistic reasoning, statistics, and combinatorics. A variety of these real-world questions can be solved by representing the question in (Boolean) formulas and associating the number of models of the formula directly with the answer to the question. Since there has been an increasing interest in practical problem solving for model counting over the past years, the Model Counting Competition was conceived in fall 2019. The competition aims to foster applications, identify new challenging benchmarks, and promote new solvers and improve established solvers for the model counting problem and versions thereof. We hope that the results can be a good indicator of the current feasibility of model counting and spark many new applications. In this article, we report on details of the Model Counting Competition 2020, about carrying out the competition, and the results. The competition encompassed three versions of the model counting problem, which we evaluated in separate tracks. The first track featured the model counting problem, which asks for the number of models of a given Boolean formula. On the second track, we challenged developers to submit programs that solve the weighted model counting problem. The last track was dedicated to projected model counting. In total, we received a surprising number of nine solvers in 34 versions from eight groups.

scholarly journals Counting Minimal Unsatisfiable Subsets

2021 ◽  
pp. 313-336
Author(s):  
Jaroslav Bendík ◽  
Kuldeep S. Meel
Keyword(s):  
Empirical Evaluation ◽  
Proper Subset ◽  
Boolean Formula ◽  
Np Hard ◽  
Sat Solvers ◽  
The Past ◽  
Recent Developments ◽  
Model Counting

AbstractGiven an unsatisfiable Boolean formula F in CNF, an unsatisfiable subset of clauses U of F is called Minimal Unsatisfiable Subset (MUS) if every proper subset of U is satisfiable. Since MUSes serve as explanations for the unsatisfiability of F, MUSes find applications in a wide variety of domains. The availability of efficient SAT solvers has aided the development of scalable techniques for finding and enumerating MUSes in the past two decades. Building on the recent developments in the design of scalable model counting techniques for SAT, Bendík and Meel initiated the study of MUS counting techniques. They succeeded in designing the first approximate MUS counter, $$\mathsf {AMUSIC}$$ AMUSIC , that does not rely on exhaustive MUS enumeration. $$\mathsf {AMUSIC}$$ AMUSIC , however, suffers from two shortcomings: the lack of exact estimates and limited scalability due to its reliance on 3-QBF solvers.In this work, we address the two shortcomings of $$\mathsf {AMUSIC}$$ AMUSIC by designing the first exact MUS counter, $$\mathsf {CountMUST}$$ CountMUST , that does not rely on exhaustive enumeration. $$\mathsf {CountMUST}$$ CountMUST circumvents the need for 3-QBF solvers by reducing the problem of MUS counting to projected model counting. While projected model counting is #NP-hard, the past few years have witnessed the development of scalable projected model counters. An extensive empirical evaluation demonstrates that $$\mathsf {CountMUST}$$ CountMUST successfully returns MUS count for 1500 instances while $$\mathsf {AMUSIC}$$ AMUSIC and enumeration-based techniques could only handle up to 833 instances.

scholarly journals GANAK: A Scalable Probabilistic Exact Model Counter

2019 ◽  
Author(s):  
Shubham Sharma ◽  
Subhajit Roy ◽  
Mate Soos ◽  
Kuldeep S. Meel
Keyword(s):  
Probabilistic Reasoning ◽  
State Of The Art ◽  
Fundamental Problem ◽  
Approximate Model ◽  
Boolean Formula ◽  
Sat Solvers ◽  
Exact Model ◽  
Universal Hashing ◽  
Model Counting ◽  
Dynamic Decomposition

Given a Boolean formula F, the problem of model counting, also referred to as #SAT, seeks to compute the number of solutions of F. Model counting is a fundamental problem with a wide variety of applications ranging from planning, quantified information flow to probabilistic reasoning and the like. The modern #SAT solvers tend to be either based on static decomposition, dynamic decomposition, or a hybrid of the two. Despite dynamic decomposition based #SAT solvers sharing much of their architecture with SAT solvers, the core design and heuristics of dynamic decomposition-based #SAT solvers has remained constant for over a decade. In this paper, we revisit the architecture of the state-of-the-art dynamic decomposition-based #SAT tool, sharpSAT, and demonstrate that by introducing a new notion of probabilistic component caching and the usage of universal hashing for exact model counting along with the development of several new heuristics can lead to significant performance improvement over state-of-the-art model-counters. In particular, we develop GANAK, a new scalable probabilistic exact model counter that outperforms state-of-the-art exact and approximate model counters sharpSAT and ApproxMC3 respectively, both in terms of PAR-2 score and the number of instances solved. Furthermore, in our experiments, the model count returned by GANAK was equal to the exact model count for all the benchmarks. Finally, we observe that recently proposed preprocessing techniques for model counting benefit exact model counters while hurting the performance of approximate model counters.

scholarly journals Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

2019 ◽  
Vol 33 ◽  
pp. 7825-7833 ◽  
Author(s):  
Pedro Zuidberg Dos Martires ◽  
Anton Dries ◽  
Luc De Raedt
Keyword(s):  
Probability Density ◽  
Probabilistic Reasoning ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Knowledge Compilation ◽  
Model Integration ◽  
Weight Functions ◽  
Density Functions ◽  
Model Counting ◽  
Weighted Model

Weighted model counting has recently been extended to weighted model integration, which can be used to solve hybrid probabilistic reasoning problems. Such problems involve both discrete and continuous probability distributions. We show how standard knowledge compilation techniques (to SDDs and d-DNNFs) apply to weighted model integration, and use it in two novel solvers, one exact and one approximate solver. Furthermore, we extend the class of employable weight functions to actual probability density functions instead of mere polynomial weight functions.

scholarly journals ADDMC: Weighted Model Counting with Algebraic Decision Diagrams

2020 ◽  
Vol 34 (02) ◽  
pp. 1468-1476
Author(s):  
Jeffrey Dudek ◽  
Vu Phan ◽  
Moshe Vardi
Keyword(s):  
Dynamic Programming ◽  
Data Structure ◽  
Normal Form ◽  
Standard Model ◽  
State Of The Art ◽  
Conjunctive Normal Form ◽  
Decision Diagrams ◽  
Boolean Formulas ◽  
Model Counting ◽  
Weighted Model

We present an algorithm to compute exact literal-weighted model counts of Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic programming and uses Algebraic Decision Diagrams as the main data structure. We implement this technique in ADDMC, a new model counter. We empirically evaluate various heuristics that can be used with ADDMC. We then compare ADDMC to four state-of-the-art weighted model counters (Cachet, c2d, d4, and miniC2D) on 1914 standard model counting benchmarks and show that ADDMC significantly improves the virtual best solver.

scholarly journals BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

2019 ◽  
Vol 33 ◽  
pp. 1592-1599 ◽  
Author(s):  
Mate Soos ◽  
Kuldeep S. Meel
Keyword(s):  
Probabilistic Reasoning ◽  
State Of The Art ◽  
Fundamental Problem ◽  
Approximate Model ◽  
Affirmative Answer ◽  
The State ◽  
Boolean Formula ◽  
Wide Range ◽  
Model Counting ◽  
Sat Solver

Given a Boolean formula φ, the problem of model counting, also referred to as #SAT is to compute the number of solutions of φ. Model counting is a fundamental problem in artificial intelligence with a wide range of applications including probabilistic reasoning, decision making under uncertainty, quantified information flow, and the like. Motivated by the success of SAT solvers, there has been surge of interest in the design of hashing-based techniques for approximate model counting for the past decade. We profiled the state of the art approximate model counter ApproxMC2 and observed that over 99.99% of time is consumed by the underlying SAT solver, CryptoMiniSat. This observation motivated us to ask: Can we design an efficient underlying CNF-XOR SAT solver that can take advantage of the structure of hashing-based algorithms and would this lead to an efficient approximate model counter? The primary contribution of this paper is an affirmative answer to the above question. We present a novel architecture, called BIRD, to handle CNF-XOR formulas arising from hashingbased techniques. The resulting hashing-based approximate model counter, called ApproxMC3, employs the BIRD framework in its underlying SAT solver, CryptoMiniSat. To the best of our knowledge, we conducted the most comprehensive study of evaluation performance of counting algorithms involving 1896 benchmarks with computational effort totaling 86400 computational hours. Our experimental evaluation demonstrates significant runtime performance improvement for ApproxMC3 over ApproxMC2. In particular, we solve 648 benchmarks more than ApproxMC2, the state of the art approximate model counter and for all the formulas where both ApproxMC2 and ApproxMC3 did not timeout and took more than 1 seconds, the mean speedup is 284.40 – more than two orders of magnitude.

scholarly journals Inference and learning in probabilistic logic programs using weighted Boolean formulas

2014 ◽  
Vol 15 (3) ◽  
pp. 358-401 ◽  
Author(s):  
DAAN FIERENS ◽  
GUY VAN DEN BROECK ◽  
JORIS RENKENS ◽  
DIMITAR SHTERIONOV ◽  
BERND GUTMANN ◽  
...  
Keyword(s):  
Graphical Model ◽  
State Of The Art ◽  
Logic Program ◽  
Knowledge Compilation ◽  
Boolean Formula ◽  
Probabilistic Logic ◽  
Logic Programs ◽  
Inference Algorithms ◽  
Boolean Formulas ◽  
Model Counting

AbstractProbabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for probabilistic logic programs. Several such tasks, such as computing the marginals, given evidence and learning from (partial) interpretations, have not really been addressed for probabilistic logic programs before. The first contribution of this paper is a suite of efficient algorithms for various inference tasks. It is based on the conversion of the program and the queries and evidence to a weighted Boolean formula. This allows us to reduce inference tasks to well-studied tasks, such as weighted model counting, which can be solved using state-of-the-art methods known from the graphical model and knowledge compilation literature. The second contribution is an algorithm for parameter estimation in the learning from interpretations setting. The algorithm employs expectation-maximization, and is built on top of the developed inference algorithms. The proposed approach is experimentally evaluated. The results show that the inference algorithms improve upon the state of the art in probabilistic logic programming, and that it is indeed possible to learn the parameters of a probabilistic logic program from interpretations.

Collective Memory: Between Values and Historical Knowledge

2020 ◽  
pp. 124-142
Author(s):  
VICTOR BURLACHUK
Keyword(s):  
Twentieth Century ◽  
Soviet Union ◽  
Collective Memory ◽  
Rapid Change ◽  
Modern Society ◽  
The State ◽  
Main Element ◽  
Rapid Decline ◽  
The Past ◽  
The Future

At the end of the twentieth century, questions of a secondary nature suddenly became topical: what do we remember and who owns the memory? Memory as one of the mental characteristics of an individual’s activity is complemented by the concept of collective memory, which requires a different method of analysis than the activity of a separate individual. In the 1970s, a situation arose that gave rise to the so-called "historical politics" or "memory politics." If philosophical studies of memory problems of the 30’s and 40’s of the twentieth century were focused mainly on the peculiarities of perception of the past in the individual and collective consciousness and did not go beyond scientific discussions, then half a century later the situation has changed dramatically. The problem of memory has found its political sound: historians and sociologists, politicians and representatives of the media have entered the discourse on memory. Modern society, including all social, ethnic and family groups, has undergone a profound change in the traditional attitude towards the past, which has been associated with changes in the structure of government. In connection with the discrediting of the Soviet Union, the rapid decline of the Communist Party and its ideology, there was a collapse of Marxism, which provided for a certain model of time and history. The end of the revolutionary idea, a powerful vector that indicated the direction of historical time into the future, inevitably led to a rapid change in perception of the past. Three models of the future, which, according to Pierre Nora, defined the face of the past (the future as a restoration of the past, the future as progress and the future as a revolution) that existed until recently, have now lost their relevance. Today, absolute uncertainty hangs over the future. The inability to predict the future poses certain challenges to the present. The end of any teleology of history imposes on the present a debt of memory. Features of the life of memory, the specifics of its state and functioning directly affect the state of identity, both personal and collective. Distortion of memory, its incorrect work, and its ideological manipulation can give rise to an identity crisis. The memorial phenomenon is a certain political resource in a situation of severe socio-political breaks and changes. In the conditions of the economic crisis and in the absence of a real and clear program for future development, the state often seeks to turn memory into the main element of national consolidation.

Introduction

2018 ◽  
Author(s):  
Gianfranco Pacchioni
Keyword(s):  
Industrial Revolution ◽  
Homo Sapiens ◽  
Modern Society ◽  
Full Time ◽  
Human Race ◽  
Hunter Gatherers ◽  
The Past ◽  
The World ◽  
The Universe ◽  
Radical Transformation

About 10,000 years ago, at the beginning of the agriculturalrevolution, on the whole earth lived between 5 and 8 million hunter-gatherers, all belonging to the Homo sapiens species. Five thousand years later, freed from the primary needs for survival, some belonging to that species enjoyed the privilege of devoting themselves to philosophical speculation and the search for transcendental truths. It was only in the past two hundred years, however, with the advent of the Industrial Revolution, that reaping nature’s secrets and answering fundamental questions posed by the Universe have become for many full-time activities, on the way to becoming a real profession. Today the number of scientists across the globe has reached and exceeded 10 million, that is, more than the whole human race 10,000 years ago. If growth continues at the current rate, in 2050 we will have 35 million people committed full-time to scientific research. With what consequences, it remains to be understood. For almost forty years I myself have been concerned with science in a continuing, direct, and passionate way. Today I perceive, along with many colleagues, especially of my generation, that things are evolving and have changed deeply, in ways unimaginable until a few years ago and, in some respects, not without danger. What has happened in the world of science in recent decades is more than likely a mirror of a similar and equally radical transformation taking place in modern society, particularly with the advent ...

The New Islamic State

2020 ◽  
Author(s):  
Farhad Khosrokhavar
Keyword(s):  
Middle East ◽  
Modern Society ◽  
Islamic State ◽  
Imagined Community ◽  
The West ◽  
Patriarchal Family ◽  
The Past ◽  
The World ◽  
The Creation

The creation of the Islamic State in Iraq and Sham (ISIS) changed the nature of jihadism worldwide. For a few years (2014–2017) it exemplified the destructive capacity of jihadism and created a new utopia aimed at restoring the past greatness and glory of the former caliphate. It also attracted tens of thousands of young wannabe combatants of faith (mujahids, those who make jihad) toward Syria and Iraq from more than 100 countries. Its utopia was dual: not only re-creating the caliphate that would spread Islam all over the world but also creating a cohesive, imagined community (the neo-umma) that would restore patriarchal family and put an end to the crisis of modern society through an inflexible interpretation of shari‘a (Islamic laws and commandments). To achieve these goals, ISIS diversified its approach. It focused, in the West, on the rancor of the Muslim migrants’ sons and daughters, on exoticism, and on an imaginary dream world and, in the Middle East, on tribes and the Sunni/Shi‘a divide, particularly in the Iraqi and Syrian societies.

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