scholarly journals Chapter 33. Satisfiability Modulo Theories

2021 ◽  
Author(s):  
Clark Barrett ◽  
Roberto Sebastiani ◽  
Sanjit A. Seshia ◽  
Cesare Tinelli
Keyword(s):  
Relevant Literature ◽  
Finite Size ◽  
Decision Procedures ◽  
Research Field ◽  
Satisfiability Modulo Theories ◽  
Practical Applications ◽  
First Order ◽  
Background Theory ◽  
Sat Solver ◽  
And Function

Applications in artificial intelligence, formal verification, and other areas have greatly benefited from the recent advances in SAT. It is often the case, however, that applications in these fields require determining the satisfiability of formulas in more expressive logics such as first-order logic. Also, these applications typically require not general first-order satisfiability, but rather satisfiability with respect to some background theory, which fixes the interpretations of certain predicate and function symbols. For many background theories, specialized methods yield decision procedures for the satisfiability of quantifier-free formulas or some subclass thereof. Specialized decision procedures have been discovered for a long and still growing list of theories with practical applications. These include the theory of equality, various theories of arithmetic, and certain theories of arrays, as well as theories of lists, tuples, records, and bit-vectors of a fixed or arbitrary finite size. The research field concerned with determining the satisfiability of formulas with respect to some background theory is called Satisfiability Modulo Theories (SMT). This chapter provides a brief overview of SMT together with references to the relevant literature for a deeper study. It begins with an overview of techniques for solving SMT problems by encodings to SAT. The rest of the chapter is mostly concerned with an alternative approach in which a SAT solver is integrated with a separate decision procedure (called a theory solver) for conjunctions of literals in the background theory. After presenting this approach as a whole, the chapter provides more details on how to construct and combine theory solvers, and discusses several extensions and enhancements.

scholarly journals AVATAR Modulo Theories

10.29007/k6tp ◽  
2018 ◽  
Author(s):  
Giles Reger ◽  
Nikolaj Bjorner ◽  
Martin Suda ◽  
Andrei Voronkov
Keyword(s):  
Theorem Proving ◽  
Satisfiability Modulo Theories ◽  
Theorem Prover ◽  
Ground Theory ◽  
Smt Solver ◽  
First Order ◽  
Proof Search ◽  
Smt Solvers ◽  
Sat Solver ◽  
A New Technique

This paper introduces a new technique for reasoning with quantifiers and theories. Traditionally, first-order theorem provers (ATPs) are well suited to reasoning with first-order problems containing many quantifiers and satisfiability modulo theories (SMT) solvers are well suited to reasoning with first-order problems in ground theories such as arithmetic. A recent development in first-order theorem proving has been the AVATAR architecture which uses a SAT solver to guide proof search based on a propositional abstraction of the first-order clause space. The approach turns a single proof search into a sequence of proof searches on (much) smaller sub-problems. This work extends the AVATAR approach to use a SMT solver in place of the SAT solver, with the effect that the first-order solver only needs to consider ground-theory-consistent sub-problems. The new architecture has been implemented using the Vampire theorem prover and Z3 SMT solver. Our experimental results, and the results of recent competitions, show that such a combination can be highly effective.

Automatically inferring loop invariants via algorithmic learning

2014 ◽  
Vol 25 (4) ◽  
pp. 892-915 ◽  
Author(s):  
YUNGBUM JUNG ◽  
SOONHO KONG ◽  
CRISTINA DAVID ◽  
BOW-YAW WANG ◽  
KWANGKEUN YI
Keyword(s):  
Decision Procedures ◽  
Satisfiability Modulo Theories ◽  
Predicate Abstraction ◽  
First Order ◽  
Fixed Set ◽  
Algorithmic Learning ◽  
Automated Technique ◽  
The Given

By combining algorithmic learning, decision procedures, predicate abstraction and simple templates for quantified formulae, we present an automated technique for finding loop invariants. Theoretically, this technique can find arbitrary first-order invariants (modulo a fixed set of atomic propositions and an underlying satisfiability modulo theories solver) in the form of the given template and exploit the flexibility in invariants by a simple randomized mechanism. In our study, the proposed technique was able to find quantified invariants for loops from the Linux source and other realistic programs. Our contribution is a simpler technique than the previous works yet with a reasonable derivation power.

scholarly journals Lower Bounds and Faster Algorithms for Equality Constraints

2020 ◽  
Author(s):  
Peter Jonsson ◽  
Victor Lagerkvist
Keyword(s):  
Lower Bounds ◽  
Constraint Satisfaction Problems ◽  
Satisfiability Modulo Theories ◽  
Infinite Domain ◽  
First Order ◽  
Fine Grained ◽  
Background Theory ◽  
Definable Relations ◽  
Np Complete ◽  
Rule Out

We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations. We prove that under the randomised exponential-time hypothesis it is not possible to find c > 1 such that a CSP over an arbitrary finite equality language is solvable in O(c^n) time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of 2^o(n log n) time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each c > 1 there exists an NP-hard equality CSP solvable in O(c^n) time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in O(c^n) time for a fixed c.

Novel Trapezoidal-Loop Piezoelectric Energy Harvester

2014 ◽  
Vol 672-674 ◽  
pp. 402-406
Author(s):  
Bing Jiang ◽  
Shuai Yuan ◽  
Xiao Hui Xu ◽  
Mao Sheng Ding ◽  
Ye Yuan ◽  
...  
Keyword(s):  
Output Voltage ◽  
Energy Harvester ◽  
Research Field ◽  
Structure Design ◽  
Loop Structure ◽  
Element Analysis ◽  
Resonant Frequencies ◽  
First Order ◽  
Microelectronic Devices ◽  
Piezoelectric Energy

In recent years, piezoelectric energy harvester which can replace the traditional battery supply has become a hot topic in global research field of microelectronic devices. Characteristics of a trapezoidal-loop piezoelectric energy harvester (TLPEH) were analyzed through finite-element analysis. The output voltage density is 4.251V/cm2 when 0.1N force is applied to the free end of ten-arm energy harvester. Comparisons of the resonant frequencies and output voltages were made. The first order resonant frequency could reach 15Hz by increasing the number of arms. Meanwhile, the output voltage is improved greatly when excited at first-order resonant frequencies. The trapezoidal-loop structure of TLPEH could enhance frequency response, which means scavenging energy more efficiently in vibration environment. The TLPEH mentioned here might be useful for the future structure design of piezoelectric energy harvester with low resonance frequency.

scholarly journals Macroscopic degeneracy and order in the 3D plaquette Ising model

2015 ◽  
Vol 29 (20) ◽  
pp. 1550109 ◽  
Author(s):  
Desmond A. Johnston ◽  
Marco Mueller ◽  
Wolfhard Janke
Keyword(s):  
Low Temperature ◽  
Magnetic Order ◽  
Finite Size ◽  
Temperature Phase ◽  
Finite Size Scaling ◽  
First Order ◽  
Magnetic Order Parameter ◽  
First Order Transition ◽  
Definition Of ◽  
Low Temperature Phase

The purely plaquette 3D Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, “fuki-nuke” order still exists and we confirm this with multi-canonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analyzing our measurements.

scholarly journals Ovarian Epithelial Cancer Stem Cells

2011 ◽  
Vol 11 ◽  
pp. 1243-1269 ◽  
Author(s):  
Irena Conic ◽  
Irena Dimov ◽  
Desanka Tasic-Dimov ◽  
Biljana Djordjevic ◽  
Vladisav Stefanovic
Keyword(s):  
Stem Cells ◽  
Cancer Stem Cells ◽  
Potential Role ◽  
Research Field ◽  
Current Evidence ◽  
Epithelial Stem Cells ◽  
Ovarian Epithelial Cancer ◽  
Cells Of Origin ◽  
Cancer Types ◽  
And Function

The last decade witnessed an explosion of interest in cancer stem cells (CSCs). The realization of epithelial ovarian cancer (EOC) as a CSC-related disease has the potential to change approaches in the treatment of this devastating disease dramatically. The etiology and early events in the progression of these carcinomas are among the least understood of all major human malignancies. Compared to the CSCs of other cancer types, the identification and study of EOC stem cells (EOCSCs) is rather difficult due to several major obstacles: the heterogeneity of tumors comprising EOCs, unknown cells of origin, and lack of knowledge considering the normal ovarian stem cells. This poses a major challenge for urgent development in this research field. This review summarizes and evaluates the current evidence for the existence of candidate normal ovarian epithelial stem cells as well as EOCSCs, emphasizing the requirement for a more definitive laboratory approach for the isolation, identification, and enrichment of EOCSCs. The present review also revisits the ongoing debate regarding other cells and tissues of origin of EOCs, and discusses early events in the pathogenesis of this disease. Finally, this review discusses the signaling pathways that are important regulators of candidate EOCSC maintenance and function, their potential role in the distinct pathogenesis of different EOC subtypes, as well as potential mechanisms and clinical relevance of EOCSC involvement in drug resistance.

Interface Potential Modeling in a Finite Crystal

2010 ◽  
Vol 107 ◽  
pp. 55-62
Author(s):  
Ernesto E. Cortés ◽  
Fernando M. Torres
Keyword(s):  
Finite Size ◽  
Electrochemical Treatment ◽  
Theoretical Interest ◽  
First Order ◽  
Interface Potential ◽  
Atomic Rearrangement

In this paper a model was proposed to calculate the interface potential of a non ideal finite crystal. Most of the research in this issue usually assume ideal conditions to work with infinite perfect crystals. The model includes a perturbative potential to consider an effect associated to finite size crystal and superficial atomic rearrangement. This effect is considered to be in a first order. The model was applied to graphite , as an example, mainly because of its theoretical interest for wastewater electrochemical treatment.

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