scholarly journals Post Mortem Analysis of SAT Solver Proofs

10.29007/gpp8 ◽  
2018 ◽  
Author(s):  
Laurent Simon
Keyword(s):  
Complex Systems ◽  
Learning Algorithms ◽  
Point Of View ◽  
Post Mortem ◽  
Learning Mechanism ◽  
Clause Learning ◽  
Sat Solver ◽  
Resolution Proofs ◽  
Final Proof

Conflict-Driven Clause Learning algorithms are well known from an engineerpoint of view. Thanks to Minisat, their designs are well understood, and mostof their implementations follow the same ideas, with essentially the samecomponents. Same heuristics, fast restarts, same learning mechanism.However, their efficiency has an important drawback: they are more and morelike complex systems and harder and harder to handle. Unfortunately, only afew works are focusing on understanding them rather than improving them. Inmost of the cases, their studies are often based on a generate and testpattern: An idea is added to an existing solver and if it improves itsefficiency the idea is published and kept. In this paper, we analyse``post-mortem'' the proofs given by one typical CDCL solver,Glucose. The originality of our approach is that we only consider it as aresolution proofs builder, and then we analyze some of the proofcharacteristics on a set of selected unsatisfiable instances, by shuffling each ofthem 200 times. We particularly focus on trying to characterize useless anduseful clauses in the proof as well as proofs shapes. We also show thatdespite their incredible efficiency, roughly 90% of the time spent in aCDCL is useless for producing the final proof.

Chapter 3. Complete Algorithms

2021 ◽  
Author(s):  
Adnan Darwiche ◽  
Knot Pipatsrisawat
Keyword(s):  
Real World ◽  
Theoretical Perspective ◽  
Point Of View ◽  
Sat Solving ◽  
Practical Point ◽  
Sat Solvers ◽  
Proof Systems ◽  
Real World Applications ◽  
Clause Learning

Complete SAT algorithms form an important part of the SAT literature. From a theoretical perspective, complete algorithms can be used as tools for studying the complexities of different proof systems. From a practical point of view, these algorithms form the basis for tackling SAT problems arising from real-world applications. The practicality of modern, complete SAT solvers undoubtedly contributes to the growing interest in the class of complete SAT algorithms. We review these algorithms in this chapter, including Davis-Putnum resolution, Stalmarck’s algorithm, symbolic SAT solving, the DPLL algorithm, and modern clause-learning SAT solvers. We also discuss the issue of certifying the answers of modern complete SAT solvers.

Modularity in Artificial Neural Networks

2011 ◽  
pp. 1095-1101
Author(s):  
Ricardo Téllez ◽  
Cecilio Angulo
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Complex Systems ◽  
Intelligent Systems ◽  
Point Of View ◽  
Main Concern ◽  
Complex Structures ◽  
Computational Point ◽  
Points Of View

The concept of modularity is a main concern for the generation of artificially intelligent systems. Modularity is an ubiquitous organization principle found everywhere in natural and artificial complex systems (Callebaut, 2005). Evidences from biological and philosophical points of view (Caelli and Wen, 1999) (Fodor, 1983), indicate that modularity is a requisite for complex intelligent behaviour. Besides, from an engineering point of view, modularity seems to be the only way for the construction of complex structures. Hence, whether complex neural programs for complex agents are desired, modularity is required. This article introduces the concepts of modularity and module from a computational point of view, and how they apply to the generation of neural programs based on modules. Two levels, strategic and tactical, at which modularity can be implemented, are identified. How they work and how they can be combined for the generation of a completely modular controller for a neural network based agent is presented.

Cities as Complex Systems

2020 ◽  
Vol 1 (2) ◽  
pp. 1-16
Author(s):  
Antonio Opromolla ◽  
Valentina Volpi
Keyword(s):  
Complex Systems ◽  
Collaborative Design ◽  
Digital Technologies ◽  
Point Of View ◽  
Urban Spaces ◽  
Economic Point ◽  
Sustainable Solutions ◽  
Human Aspects ◽  
The People ◽  
Hybrid Spaces

Cities can be considered as “complex systems,” since they are characterized by multiple connected elements and by relations among them that are not always recognizable. The massive presence of digital technologies in urban spaces that transform them into “hybrid” spaces makes cities even more complex. This article shows some of the challenges that arise in this new context (e.g., rethinking the people experience in the urban spaces; developing new “urban competences” using in an effective way the large amount of produced data; focusing on the human aspects rather than the technological ones; thinking of sustainable solutions from the environmental, social, and economic point of view; etc.), and it proposes the application of collaborative design frameworks that can offer specific tools and methodologies to face them.

Constraining solution space to improve generalization

1997 ◽  
Vol 20 (1) ◽  
pp. 67-68
Author(s):  
John A. Bullinaria
Keyword(s):  
Learning Algorithms ◽  
Solution Space ◽  
Local Information ◽  
Learning Processes ◽  
Point Of View ◽  
Heavy Duty ◽  
Hidden Regularities ◽  
Evolutionary Point

I suggest that the difficulties inherent in discovering the hidden regularities in realistic (type-2) problems can often be resolved by learning algorithms employing simple constraints (such as symmetry and the importance of local information) that are natural from an evolutionary point of view. Neither “heavy-duty nativism” nor “representational recoding” appear to offer totally appropriate descriptions of such natural learning processes.

Complex Systems Study as Biology

1998 ◽  
Vol 12 (03) ◽  
pp. 245-256 ◽  
Author(s):  
Y. Oono
Keyword(s):  
Complex Systems ◽  
Point Of View

If we pay serious and conscientious attention to the connotation of the word "complexity", study of complex systems must basically be biology. Basic questions are raised from this point of view.

A complex biological system: the fly's visual module

2007 ◽  
Vol 366 (1864) ◽  
pp. 345-357 ◽  
Author(s):  
Murilo S Baptista ◽  
Lirio O.B de Almeida ◽  
Jan F.W Slaets ◽  
Roland Köberle ◽  
Celso Grebogi
Keyword(s):  
Probability Measure ◽  
Complex Systems ◽  
Visual System ◽  
Lyapunov Exponents ◽  
Biological System ◽  
Dimensional Space ◽  
Point Of View ◽  
Two Dimensional ◽  
Complex Biological System

Is the characterization of biological systems as complex systems in the mathematical sense a fruitful assertion? In this paper we argue in the affirmative, although obviously we do not attempt to confront all the issues raised by this question. We use the fly's visual system as an example and analyse our experimental results of one particular neuron in the fly's visual system from this point of view. We find that the motion-sensitive ‘H1’ neuron, which converts incoming signals into a sequence of identical pulses or ‘spikes’, encodes the information contained in the stimulus into an alphabet composed of a few letters. This encoding occurs on multilayered sets, one of the features attributed to complex systems . The conversion of intervals between consecutive occurrences of spikes into an alphabet requires us to construct a generating partition . This entails a one-to-one correspondence between sequences of spike intervals and words written in the alphabet. The alphabet dynamics is multifractal both with and without stimulus, though the multifractality increases with the stimulus entropy. This is in sharp contrast to models generating independent spike intervals, such as models using Poisson statistics, whose dynamics is monofractal. We embed the support of the probability measure, which describes the distribution of words written in this alphabet, in a two-dimensional space, whose topology can be reproduced by an M-shaped map. This map has positive Lyapunov exponents, indicating a chaotic-like encoding.

scholarly journals FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

2020 ◽  
Vol 34 (02) ◽  
pp. 1552-1560
Author(s):  
Anastasios Kyrillidis ◽  
Anshumali Shrivastava ◽  
Moshe Vardi ◽  
Zhiwei Zhang
Keyword(s):  
Boolean Functions ◽  
Continuous Optimization ◽  
Conjunctive Normal Form ◽  
Cardinality Constraints ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Algebraic Framework ◽  
Clause Learning ◽  
Sat Solver ◽  
Analysis Of Boolean Functions

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side—especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers—has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF), have become quite mature, SAT solvers that are effective on other types of constraints (e.g., cardinality constraints and XORs) are less well-studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time.To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Empirical results demonstrate that FourierSAT is more robust than other solvers on certain classes of benchmarks.

scholarly journals Cognitive Networks: Interactivity, Intersubjectivity, and Synergy

2018 ◽  
Vol 20 (1) ◽  
pp. 52-78
Author(s):  
Helena Knyazeva
Keyword(s):  
Complex Systems ◽  
Cognitive Science ◽  
Cognitive Processes ◽  
Network Science ◽  
Cognitive Maps ◽  
Cognitive Networks ◽  
Point Of View ◽  
Network Structures ◽  
Cognitive Coherence ◽  
Cognitive Niches

Some properties of cognitive networks are discussed in the article in the context of the modern achievements of the network science. It is the study in network structures and their surprising properties that gives a new impetus to the development of the theory of complex systems (synergetics). The analysis of cognitive processes from the point of view of the network structures that arise in them not only fits with such concepts already existing in cognitive science and epistemology, as cognitive niches, cognitive maps, cognitive coherence, etc.), but also brings some new aspects to the understanding of interactivity, intersubjectivity, synergy in cognition and creative activities, empathy.

scholarly journals Exploring Education and Education Reforms from the Complex Systems Point of View

2018 ◽  
Vol 56 (1) ◽  
pp. 1-15
Author(s):  
Ljubinka Joksimović ◽  
Slavica Manić
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
Education System ◽  
Educational Practice ◽  
Point Of View ◽  
Complex Nature ◽  
Education Reforms ◽  
Policy Makers ◽  
The World ◽  
Theory Of Complexity

Abstract The main motivation for this paper is that a negligible number of reforms in education systems, initiated all over the world, proved to be successful in terms of bringing desired results in promoting educational practice and its final goal - the promotion of students’ learning and knowledge. Regarding the education system and its reform a change of paradigm has recently happened. In some cases, changes were made gradually, whereas in other cases it was completely abandonment of treating them as complicated systems with simple interventions and solutions toward the recognition and respect of their true complex nature. So, this reviewed paper explores new insights and tools derived from the theory of complexity. They can help to better understand and navigate the education system and its reform. Becoming familiarised with methodological implications of viewing the education system and its reform as complex system is recommendation for different stakeholders included in education system, such as teachers, students, researchers, administrators and policy makers. Advance awareness of both urgency and opportunities of analysing and respecting the education system as a complex system would contribute to better understanding the essence of dynamic wholeness of education and, for sure, would provide desired results of educational reform. For all of us that means more successful coping with the world characterised by a growing number of complex systems with growing intensity.

Pachymeningitis Interna Hæmorrhagica as a Cause of Death

1915 ◽  
Vol 61 (254) ◽  
pp. 443-446
Author(s):  
H. D. MacPhail
Keyword(s):  
Clinical Study ◽  
Cause Of Death ◽  
Point Of View ◽  
Post Mortem ◽  
Pathological Conditions ◽  
Morbid Anatomy ◽  
Clinical Records ◽  
Morbid State ◽  
Morbid Process

There are some pathological conditions which, though of considerable interest to the student of morbid anatomy, appear to have very little importance from the point of view of clinical study. The reason for this, sometimes at least, lies in the fact that it is difficult, if not impossible, to diagnose the onset and follow the progress of the morbid process during the life of the patient. Pachymeningitis interna hemorrhagica is essentially a condition of this kind. It is a morbid state which has been named and described for years, and yet it is a condition the diagnosis of which during life is extremely difficult. As a rule, when it is demonstrated at the post mortem, the clinical records of the case furnish us with no definite information suggestive of its presence. Often when symptoms point to the likelihood of its presence no lesion is found, while it occurs in cases which during life showed nothing special to indicate the possibility of such a condition.

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