Boolean Satisfiability in Electronic Design Automation

Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT “packages” are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

In various areas of computer science, we deal with a set of constraints to be satisfied. If the constraints cannot be satisfied simultaneously, it is desirable to identify the core problems among them. Such cores are called minimal unsatisfiable subsets (MUSes). The more MUSes are identified, the more information about the conflicts among the constraints is obtained. However, a full enumeration of all MUSes is in general intractable due to the large number (even exponential) of possible conflicts. Moreover, to identify MUSes algorithms must test sets of constraints for their simultaneous satisfiabilty. The type of the test depends on the application domains. The complexity of tests can be extremely high especially for domains like temporal logics, model checking, or SMT. In this paper, we propose a recursive algorithm that identifies MUSes in an online manner (i.e., one by one) and can be terminated at any time. The key feature of our algorithm is that it minimizes the number of satisfiability tests and thus speeds up the computation. The algorithm is applicable to an arbitrary constraint domain and its effectiveness demonstrates itself especially in domains with expensive satisfiability checks. We benchmark our algorithm against state of the art algorithm on Boolean and SMT constraint domains and demonstrate that our algorithm really requires less satisfiability tests and consequently finds more MUSes in given time limits

GRASP: A New Search Algorithm for Satisfiability

This paper introduces GRASP (Generic search Algorithm J3r the Satisfiabilily Problem), an integrated algorithmic J3amework 30r SAT that unifies several previously proposed searchpruning techniques and jcilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'ecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Einally, straighrward bookkeeping of the causali y chains leading up to conflicts a/lows GRASP to identij) assignments that are necessary jr a solution to be found. Experimental results obtained jom a large number of benchmarks, including many J3om the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely ejctive jr a large number of representative classes of SAT instances

Conflict Analysis in Search Algorithms for Satisfiability

This paper introduces GRASP (Generic search Algorithm jr the Satisfiabili{y Problem), a new search algorithm jr Propositional Satisfiabili{y (SAT). GRASP incorporates several search-pruning techniques, some of which are specific to SAT, whereas others find equivalent in other fields of Artificial Intelligence. GRASP is premised on the inevitabili{y of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'gecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straigh&rward bookkeeping of the causali {y chains leading up to conflicts allows GRASP to identij) assignments that are necessary jr a solution to be jund. Experimental results obtained jom a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely efctive jr a large number of representative classes of SAT instances

Diagnose network failures via data-plane analysis

Diagnosing problems in networks is a time-consuming and error-prone process. Previous tools to assist operators primarily focus on analyzing control plane configuration. Configuration analysis is limited in that it cannot find bugs in router software, and is harder to generalize across protocols since it must model complex configuration languages and dynamic protocol behavior. This paper studies an alternate approach: diagnosing problems through static analysis of the data plane. This approach can catch bugs that are invisible at the level of configuration files, and simplifies unified analysis of a network across many protocols and implementations. We present Anteater, a tool for checking invariants in the data plane. Anteater translates high-level network invariants into boolean satisfiability problems, checks them against network state using a SAT solver, and reports counterexamples if violations have been found. Applied to a large campus network, Anteater revealed 23 bugs, including forwarding loops and stale ACL rules, with only five false positives. Nine of these faults are being fixed by campus network operators