Beaver: Engineering an Efficient SMT Solver for Bit-Vector Arithmetic

Jha, Susmit; Limaye, Rhishikesh; Seshia, Sanjit A.

doi:10.1007/978-3-642-02658-4_53

Cited by 51 publications

(41 citation statements)

References 12 publications

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“…Furthermore, the SAT-based solving approach continues to find various new application domains today. Conflict-driven clause learning (CDCL) SAT solvers are at the heart of SMT solvers, and in some cases such as the theory of bit-vectors, most state-of-the-art SMT solvers are based on bit-blasting and use pure SAT solvers for actual solving (including [21,15,11,10,31,12]). This gives motivation for developing even more efficient solving techniques for SAT.…”

Section: Introductionmentioning

confidence: 99%

Simulating Circuit-Level Simplifications on CNF

2011

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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 2 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.

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Section: Introductionmentioning

confidence: 99%

Simulating Circuit-Level Simplifications on CNF

2011

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“…There has been a lot of work on optimal encodings for specific kinds of constraints like cardinality constraints [1], sequence constraints [14], verification of microprocessors [55]. There is also some work on logic minimization techniques like Beaver [41]. But, to our knowledge, we are the first ones to generate domain specific encodings that are propagation complete and minimal for multiple challenging domains using program synthesis technology.…”

Section: Reducing Encodings Sizementioning

confidence: 99%

“…OptCNF can be extended to other SMT solvers besides CVC4 such as Z3 [21], Beaver [41], Boolector [15] and Yices [23]. In Beaver and Boolector, intermediate data structures like And-Inverter graphs (AIGs) are employed and are later on transformed to CNF efficiently.…”

Section: Other Smt Solversmentioning

confidence: 99%

Synthesis of Domain Specific CNF Encoders for Bit-Vector Solvers

Inala

Singh

Solar-Lezama

2016

Theory and Applications of Satisfiability Testing – SAT 2016

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SMT solvers are at the heart of a number of software engineering tools. These SMT solvers use a SAT solver as the back-end and convert the high-level constraints given by the user down to low-level boolean formulas that can be efficiently mapped to CNF clauses and fed into a SAT solver. Current SMT solvers are designed to be general purpose solvers that are suited to a wide range of problems. However, SAT solvers are very non-deterministic and hence, it is difficult to optimize a general purpose solver across all different problems. In this thesis, we propose a system that can automatically generate parts of SMT solvers in a way that is tailored to particular problem domains. In particular, we target the translation from high-level constraints to CNF clauses which is one of the crucial parts of all SMT solvers. We achieve this goal by using a combination of program synthesis and machine learning techniques. We use a program synthesis tool called Sketch to generate optimal encoding rules for this translation and then use auto-tuning to only select the subset of these encodings that actually improve the performance for a particular class of problems.Using this technique, the thesis shows that we can improve upon the basic encoding strategy used by CVC4 (a state of the art SMT solver). We can automatically generate variants of the solver tailored to different domains of problems represented in the bit-vector benchmark suite from the SMT competition 2015.

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“…SMT solvers for the theory of quantifier-free bit-vector arithmetic [8], as we will see in this section, can also model equations (1)-(4) and have the advantage that they can also encode more easily the bound on the number of arcs in the C-net, as well as some other constraints (see Sect. 3.6).…”

Section: Solving Linear Constraints Using Smtmentioning

confidence: 99%

An SMT-Based Discovery Algorithm for C-Nets

Solé

Carmona

2012

Lecture Notes in Computer Science

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Abstract. Recently, Causal nets have been proposed as a suitable model for process discovery, due to their declarative semantics and the great expressiveness they possess. In this paper we propose an algorithm to discover a causal net from a set of traces. It is based on encoding the problem as a Satisfiability Modulo Theories (SMT) formula, and uses a binary search strategy to optimize the derived model. The method has been implemented in a prototype tool that interacts with an SMT solver. The experimental results obtained witness the capability of the approach to discover complex behavior in limited time.

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Beaver: Engineering an Efficient SMT Solver for Bit-Vector Arithmetic

Cited by 51 publications

References 12 publications

Simulating Circuit-Level Simplifications on CNF

Simulating Circuit-Level Simplifications on CNF

Synthesis of Domain Specific CNF Encoders for Bit-Vector Solvers

An SMT-Based Discovery Algorithm for C-Nets

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