求解QBF 问题的启发式调查传播算法

提出了一种启发式调查传播算法,并基于该算法设计了一种QBF(quantified Boolean formulae)求解器——HSPQBF(heuristic survey propagation algorithm for solving QBF)系统.它将Survey Propagation信息传递方法应用到QBF求解问题中.利用Survey Propagation作为启发式引导DPLL(Davis,Putnam,Logemann and Loveland)算法,选择合适的变量进行分支,从而可以减小搜索空间,并减少算法回退的次数.在分支处理过程中,HSPQBF系统结合了单元传播、冲突学习和满足蕴涵学习等一些优秀的QBF求解技术,从而能够提高QBF问题的求解效率.实验结果表明,HSPQBF无论在随机问题上还是在QBF标准测试问题上都有很好的表现,验证了调查传播技术在QBF问题求解中的实际价值.     

Model generation for quantified formulas with application to test data generation

We present a new model generation approach and technique for solving first-order logic (FOL) formulas with quantifiers in unbounded domains. Model generation is important, e.g., for test data generation based on test data constraints and for counterexample generation in formal verification. In such scenarios, quantified FOL formulas have to be solved stemming, e.g., from formal specifications. Satisfiability modulo theories (SMT) solvers are considered as the state-of-the-art techniques for generating models of FOL formulas. Handling of quantified formulas in the combination of theories is, however, sometimes a problem. Our approach addresses this problem and can solve formulas that were not solvable before using SMT solvers. We present the model generation algorithm and show how to convert a representation of a model into a test preamble for state initialization with test data. A prototype of this algorithm is implemented in the formal verification and test generation tool KeY.     

A solver for QBFs in negation normal form

Various problems in artificial intelligence can be solved by translating them into a quantified boolean formula (QBF) and evaluating the resulting encoding. In this approach, a QBF solver is used as a black box in a rapid implementation of a more general reasoning system. Most of the current solvers for QBFs require formulas in prenex conjunctive normal form as input, which makes a further translation necessary, since the encodings are usually not in a specific normal form. This additional step increases the number of variables in the formula or disrupts the formula’s structure. Moreover, the most important part of this transformation, prenexing, is not deterministic. In this paper, we focus on an alternative way to process QBFs without these drawbacks and describe a solver, $\ensuremath{\sf qpro}Various problems in artificial intelligence can be solved by translating them into a quantified boolean formula (QBF) and evaluating the resulting encoding. In this approach, a QBF solver is used as a black box in a rapid implementation of a more general reasoning system. Most of the current solvers for QBFs require formulas in prenex conjunctive normal form as input, which makes a further translation necessary, since the encodings are usually not in a specific normal form. This additional step increases the number of variables in the formula or disrupts the formula’s structure. Moreover, the most important part of this transformation, prenexing, is not deterministic. In this paper, we focus on an alternative way to process QBFs without these drawbacks and describe a solver, , which is able to handle arbitrary formulas. To this end, we extend algorithms for QBFs to the non-normal form case and compare with the leading normal form provers on several problems from the area of artificial intelligence. We prove properties of the algorithms generalized to non-clausal form by using a novel approach based on a sequent-style formulation of the calculus. This paper is based on an extended abstract presented at ECAI 2006 (see [16]). This work was supported by the Austrian Science Fund (FWF) under grant P18019, the Austrian Academic Exchange Service (?AD) under grant Amadée 2/2006, and by the Austrian Federal Ministry of Transport, Innovation and Technology BMVIT and the Austrian Research Promotion Agency FFG under grant FIT-IT-810806.     

Compressing BMC Encodings with QBF

Symbolic model checking is PSPACE complete. Since QBF is the standard PSPACE complete problem, it is most natural to encode symbolic model checking problems as QBF formulas and then use QBF decision procedures to solve them. We discuss alternative encodings for unbounded and bounded safety checking into SAT and QBF. One contribution is a linear encoding of simple path constraints, which usually are necessary to make k-induction complete. Our experimental results show that indeed a large reduction in the size of the generated formulas can be obtained. However, current QBF solvers seem not to be able to take advantage of these compact formulations. Despite these mostly negative results the availability of these benchmarks will help improve the state of the art of QBF solvers and make QBF based symbolic model checking a viable alternative.     

Unified QBF certification and its applications

Quantified Boolean formulae (QBF) allow compact encoding of many decision problems. Their importance motivated the development of fast QBF solvers. Certifying the results of a QBF solver not only ensures correctness, but also enables certain synthesis and verification tasks. To date the certificate of a true formula can be in the form of either a syntactic cube-resolution proof or a semantic Skolem-function model whereas that of a false formula is only in the form of a syntactic clause-resolution proof. The semantic certificate for a false QBF is missing, and the syntactic and semantic certificates are somewhat unrelated. This paper identifies the missing Herbrand-function countermodel for false QBF, and strengthens the connection between syntactic and semantic certificates by showing that, given a true QBF, its Skolem-function model is derivable from its cube-resolution proof of satisfiability as well as from its clause-resolution proof of unsatisfiability under formula negation. Consequently Skolem-function derivation can be decoupled from special Skolemization-based solvers and computed from standard search-based ones. Experimental results show strong benefits of the new method.     

Reasoning on constraints in CLP(FD)

Constraint Logic Programming solvers on finite domains (CLP(FD) solvers) use constraints to prune those combinations of assignments which cannot appear in any consistent solution. There are applications, such as temporal reasoning or scheduling, requiring some form of qualitative reasoning where constraints can be changed (restricted) during the computation or even chosen when disjunction occurs. We embed in a (CLP(FD) solver the concept of constraints as first class objects. In the extended language, variables range over finite domains of objects (e.g., integers) and relation variables range over finite domains of relation symbols. We define operations and constraints on the two sorts of variables and one constraint linking the two. We first present the extension as a general framework, then we propose two specializations on finite domains of integers and of sets. Programming examples are given, showing the advantages of the extension proposed from both a knowledge representation and an operational viewpoint.     

Solving quantified constraint satisfaction problems

We make a number of contributions to the study of the Quantified Constraint Satisfaction Problem (QCSP). The QCSP is an extension of the constraint satisfaction problem that can be used to model combinatorial problems containing contingency or uncertainty. It allows for universally quantified variables that can model uncertain actions and events, such as the unknown weather for a future party, or an opponent's next move in a game. In this paper we report significant contributions to two very different methods for solving QCSPs. The first approach is to implement special purpose algorithms for QCSPs; and the second is to encode QCSPs as Quantified Boolean Formulas and then use specialized QBF solvers. The discovery of particularly effective encodings influenced the design of more effective algorithms: by analyzing the properties of these encodings, we identify the features in QBF solvers responsible for their efficiency. This enables us to devise analogues of these features in QCSPs, and implement them in special purpose algorithms, yielding an effective special purpose solver, QCSP-Solve. Experiments show that this solver and a highly optimized QBF encoding are several orders of magnitude more efficient than the initially developed algorithms. A final, but significant, contribution is the identification of flaws in simple methods of generating random QCSP instances, and a means of generating instances which are not known to be flawed.     

Answer Set Programming Based on Propositional Satisfiability

Answer set programming (ASP) emerged in the late 1990s as a new logic programming paradigm that has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced. All these reductions, however, are limited to a subclass of logic programs or introduce new variables or may produce exponentially bigger propositional formulas. In this paper, we present a SAT-based procedure, called ASPSAT, that (1) deals with any (nondisjunctive) logic program, (2) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (3) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASPSAT. From a practical perspective, we have (1) implemented ASPSAT in Cmodels, (2) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (3) conducted an extensive comparative analysis involving other state-of-the-art answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered and that the reasoning strategies that work best on ‘small but hard’ problems are ineffective on ‘big but easy’ problems and vice versa.     

COMPSPEN:对形状性质与数据约束进行融合推理的分离逻辑求解器

分离逻辑是经典霍尔逻辑的针对操作指针和动态数据结构的扩展,已经广泛用于对基础软件(比如操作系统内核等)的分析与验证.分离逻辑约束自动求解是提升对操作指针和动态数据结构的程序的验证的自动化程度的重要手段.针对动态数据结构的验证一般同时涉及形状性质(比如单链表、双链表、树等)和数据性质(比如有序性、数据不变性等).主要介绍能对动态数据结构的形状性质与数据约束进行融合推理的分离逻辑求解器COMPSPEN.首先介绍COMPSPEN的理论基础,包括能够同时描述线性动态数据结构的形状性质和数据约束的分离逻辑子集SLID_data、SLID_data的可满足性和蕴涵问题的判定算法.然后,介绍COMPSPEN工具的基本框架.最后,使用COMPSPEN工具进行了实例研究.收集整理了600个测试用例,在这600个测试用例上将COMPSPEN与已有的主流分离逻辑求解器Asterix、S2S、Songbird、SPEN进行了比较.实验结果表明COMPSPEN是唯一能够求解含有集合数据约束的分离逻辑求解器,而且总体来讲,能对线性数据结构上的同时含有形状性质和线性算术数据约...     

Conformant planning as a case study of incremental QBF solving

We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of QBFs. To solve this sequence of successively constructed QBFs, we use our general-purpose incremental QBF solver DepQBF. Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase as well as in the solving phase. We also present experiments with incremental preprocessing techniques that are based on blocked clause elimination (QBCE). QBCE allows to eliminate certain clauses from a QBF in a satisfiability preserving way. We implemented the QBCE-based techniques in DepQBF in three variants: as preprocessing, as inprocessing (which extends preprocessing by taking into account variable assignments that were fixed by the QBF solver), and as a novel dynamic approach where QBCE is tightly integrated in the solving process. For DepQBF, experimental results show that incremental QBF solving with incremental QBCE outperforms incremental QBF solving without QBCE, which in turn outperforms nonincremental QBF solving. For the first time we report on incremental QBF solving with incremental QBCE as inprocessing. Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.     

Bounded model checking of software using SMT solvers instead of SAT solvers

C bounded model checking (cbmc) has proved to be a successful approach to automatic software analysis. The key idea is to (i) build a propositional formula whose models correspond to program traces (of bounded length) that violate some given property and (ii) use state-of-the-art SAT solvers to check the resulting formulae for satisfiability. In this paper, we propose a generalisation of the cbmc approach on the basis of an encoding into richer (but still decidable) theories than propositional logic. We show that our approach may lead to considerably more compact formulae than those obtained with cbmc. We have built a prototype implementation of our technique that uses a satisfiability modulo theories (SMT) solver to solve the resulting formulae. Computer experiments indicate that our approach compares favourably with—and on some significant problems outperforms—cbmc.     

Simulating Circuit-Level Simplifications on CNF

Boolean satisfiability (SAT) and its extensions have become a core technology in many application domains, such as planning and formal verification, and continue finding various new application domains today. The SAT-based approach divides into three steps: encoding, preprocessing, and search. It is often argued that by encoding arbitrary Boolean formulas in conjunctive normal form (CNF), structural properties of the original problem are not reflected in the CNF. This should result in the fact that CNF-level preprocessing and SAT solver techniques have an inherent disadvantage compared to related techniques applicable on the level of more structural SAT instance representations such as Boolean circuits. Motivated by this, various simplification techniques and intricate CNF encodings for circuit-level SAT instance representations have been proposed. On the other hand, based on the highly efficient CNF-level clause learning SAT solvers, there is also strong support for the claim that CNF is sufficient as an input format for SAT solvers. In this work we study the effect of CNF-level simplification techniques, focusing on SatElite-style variable elimination (VE) and what we call blocked clause elimination (BCE). We show that BCE is surprisingly effective both in theory and in practice on CNF formulas resulting from a standard CNF encoding for circuits: without explicit knowledge of the underlying circuit structure, it achieves the same level of simplification as a combination of circuit-level simplifications and previously suggested polarity-based CNF encodings. We also show that VE can achieve many of the same effects as BCE, but not all. On the other hand, it turns out that VE and BCE are indeed partially orthogonal techniques. We also study the practical effects of combining BCE and VE for reducing the size of formulas and on the running times of state-of-the-art SAT solvers. Furthermore, we address the problem of how to construct original witnesses to satisfiable CNF formulas when applying a combination of BCE and VE.     

Propagation engine prototyping with a domain specific language

Constraint propagation is at the heart of constraint solvers. Two main trends co-exist for its implementation: variable-oriented propagation engines and constraint-oriented propagation engines. Those two approaches ensure the same level of local consistency but their efficiency (computation time) can be quite different depending on the instance solved. However, it is usually accepted that there is no best approach in general, and modern constraint solvers implement only one. In this paper, we would like to go a step further providing a solver independent language at the modeling stage to enable the design of propagation engines. We validate our proposal with a reference implementation based on the Choco solver and the MiniZinc constraint modeling language.     

Solving satisfiability problems with preferences

Propositional satisfiability (SAT) is a success story in Computer Science and Artificial Intelligence: SAT solvers are currently used to solve problems in many different application domains, including planning and formal verification. The main reason for this success is that modern SAT solvers can successfully deal with problems having millions of variables. All these solvers are based on the Davis–Logemann–Loveland procedure (dll). In its original version, dll is a decision procedure, but it can be very easily modified in order to return one or all assignments satisfying the input set of clauses, assuming at least one exists. However, in many cases it is not enough to compute assignments satisfying all the input clauses: Indeed, the returned assignments have also to be “optimal” in some sense, e.g., they have to satisfy as many other constraints—expressed as preferences—as possible. In this paper we start with qualitative preferences on literals, defined as a partially ordered set (poset) of literals. Such a poset induces a poset on total assignments and leads to the definition of optimal model for a formula ψ as a minimal element of the poset on the models of ψ. We show (i) how dll can be extended in order to return one or all optimal models of ψ (once converted in clauses and assuming ψ is satisfiable), and (ii) how the same procedures can be used to compute optimal models wrt a qualitative preference on formulas and/or wrt a quantitative preference on literals or formulas. We implemented our ideas and we tested the resulting system on a variety of very challenging structured benchmarks. The results indicate that our implementation has comparable performances with other state-of-the-art systems, tailored for the specific problems we consider.     

MathSAT: Tight Integration of SAT and Mathematical Decision Procedures

Recent improvements in propositional satisfiability techniques (SAT) made it possible to tackle successfully some hard real-world problems (e.g., model-checking, circuit testing, propositional planning) by encoding into SAT. However, a purely Boolean representation is not expressive enough for many other real-world applications, including the verification of timed and hybrid systems, of proof obligations in software, and of circuit design at RTL level. These problems can be naturally modeled as satisfiability in linear arithmetic logic (LAL), that is, the Boolean combination of propositional variables and linear constraints over numerical variables. In this paper we present MathSAT, a new, SAT-based decision procedure for LAL, based on the (known approach) of integrating a state-of-the-art SAT solver with a dedicated mathematical solver for LAL. We improve MathSAT in two different directions. First, the top‐level line procedure is enhanced and now features a tighter integration between the Boolean search and the mathematical solver. In particular, we allow for theory-driven backjumping and learning, and theory-driven deduction; we use static learning in order to reduce the number of Boolean models that are mathematically inconsistent; we exploit problem clustering in order to partition mathematical reasoning; and we define a stack-based interface that allows us to implement mathematical reasoning in an incremental and backtrackable way. Second, the mathematical solver is based on layering; that is, the consistency of (partial) assignments is checked in theories of increasing strength (equality and uninterpreted functions, linear arithmetic over the reals, linear arithmetic over the integers). For each of these layers, a dedicated (sub)solver is used. Cheaper solvers are called first, and detection of inconsistency makes call of the subsequent solvers superfluous. We provide a through experimental evaluation of our approach, by taking into account a large set of previously proposed benchmarks. We first investigate the relative benefits and drawbacks of each proposed technique by comparison with respect to a reference option setting. We then demonstrate the global effectiveness of our approach by a comparison with several state-of-the-art decision procedures. We show that the behavior of MathSAT is often superior to its competitors, both on LAL and in the subclass of difference logic. This work has been partly supported by ISAAC, a European-sponsored project, contract no. AST3-CT-2003-501848; by ORCHID, a project sponsored by Provincia Autonoma di Trento; and by a grant from Intel Corporation. The work of T. Junttila has also been supported by the Academy of Finland, project 53695. S. Schulz has also been supported by a grant of the Italian Ministero dell'Istruzione, dell'Università e della Ricerca and the University of Verona.     

IPSS: A Hybrid Approach to Planning and Scheduling Integration

Recently, the areas of planning and scheduling in artificial intelligence (AI) have witnessed a big push toward their integration in order to solve complex problems. These problems require both reasoning on which actions are to be performed as well as their precedence constraints (planning) and the reasoning with respect to temporal constraints (e.g., duration, precedence, and deadline); those actions should satisfy the resources they use (scheduling). This paper describes IPSS (integrated planning and scheduling system), a domain independent solver that integrates an AI planner that synthesizes courses of actions with constraint-based techniques that reason based upon time and resources. IPSS is able to manage not only simple precedence constraints, but also more complex temporal requirements (as the Allen primitives) and multicapacity resource usage/consumption. The solver is evaluated against a set of problems characterized by the use of multiple agents (or multiple resources) that have to perform tasks with some temporal restrictions in the order of the tasks or some constraints in the availability of the resources. Experiments show how the integrated reasoning approach improves plan parallelism and gains better makespans than some state-of-the-art planners where multiple agents are represented as additional fluents in the problem operators. It also shows that IPSS is suitable for solving real domains (i.e., workflow problems) because it is able to impose temporal windows on the goals or set a maximum makespan, features that most of the planners do not yet incorporate     

Evaluating ASP and Commercial Solvers on the CSPLib

This paper deals with four solvers for combinatorial problems: the commercial state-of-the-art solver ILOG oplstudio, and the research answer set programming (ASP) systems dlv, smodels and cmodels. The first goal of this research is to evaluate the relative performance of such systems when used in a purely declarative way, using a reproducible and extensible experimental methodology. In particular, we consider a third-party problem library, i.e., the CSPLib, and uniform rules for modelling and instance selection. The second goal is to analyze the marginal effects of popular reformulation techniques on the various solving technologies. In particular, we consider structural symmetry breaking, the adoption of global constraints, and the addition of auxiliary predicates. Finally, we evaluate, on a subset of the problems, the impact of numbers and arithmetic constraints on the different solving technologies. Results show that there is not a single solver winning on all problems, and that reformulation is almost always beneficial: symmetry-breaking may be a good choice, but its complexity has to be carefully chosen, by taking into account also the particular solver used. Global constraints often, but not always, help opl, and the addition of auxiliary predicates is usually worth, especially when dealing with ASP solvers. Moreover, interesting synergies among the various modelling techniques exist.     

Scalable satisfiability checking and test data generation from modeling diagrams

We explore the automatic generation of test data that respect constraints expressed in the Object-Role Modeling (ORM) language. ORM is a popular conceptual modeling language, primarily targeting database applications, with significant uses in practice. The general problem of even checking whether an ORM diagram is satisfiable is quite hard: restricted forms are easily NP-hard and the problem is undecidable for some expressive formulations of ORM. Brute-force mapping to input for constraint and SAT solvers does not scale: state-of-the-art solvers fail to find data to satisfy uniqueness and mandatory constraints in realistic time even for small examples. We instead define a restricted subset of ORM that allows efficient reasoning yet contains most constraints overwhelmingly used in practice. We show that the problem of deciding whether these constraints are consistent (i.e., whether we can generate appropriate test data) is solvable in polynomial time, and we produce a highly efficient (interactive speed) checker. Additionally, we analyze over 160 ORM diagrams that capture data models from industrial practice and demonstrate that our subset of ORM is expressive enough to handle their vast majority.     

Empirical hardness of finding optimal Bayesian network structures: algorithm selection and runtime prediction

Various algorithms have been proposed for finding a Bayesian network structure that is guaranteed to maximize a given scoring function. Implementations of state-of-the-art algorithms, solvers, for this Bayesian network structure learning problem rely on adaptive search strategies, such as branch-and-bound and integer linear programming techniques. Thus, the time requirements of the solvers are not well characterized by simple functions of the instance size. Furthermore, no single solver dominates the others in speed. Given a problem instance, it is thus a priori unclear which solver will perform best and how fast it will solve the instance. We show that for a given solver the hardness of a problem instance can be efficiently predicted based on a collection of non-trivial features which go beyond the basic parameters of instance size. Specifically, we train and test statistical models on empirical data, based on the largest evaluation of state-of-the-art exact solvers to date. We demonstrate that we can predict the runtimes to a reasonable degree of accuracy. These predictions enable effective selection of solvers that perform well in terms of runtimes on a particular instance. Thus, this work contributes a highly efficient portfolio solver that makes use of several individual solvers.