This paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), a new search algorithm for Propositional Satisfiability (SAT). GRASP incorporates several search-pruning techniques that proved to be quite powerful on a wide variety of SAT problems. Some of these techniques are specific to SAT, whereas others are similar in spirit to approaches in other fields of Artificial Intelligence. GRASP is premised on the inevitability of conflicts during the search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack nonchronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by "recording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.

/pdf/grasp-a-search-algorithm-for-propositional-satisfiability-3nd8josgc5.pdf

GRASP: a search algorithm for propositional satisfiability

This paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), an integrated algorithmic framework for SAT that unifies several previously proposed search-pruning techniques and facilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishing feature 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 "recording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks, including many from the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.

https://eprints.soton.ac.uk/262031/1/jpms-iccad96.pdf

GRASP—a new search algorithm for satisfiability

The author describes the Boolean satisfiability method for generating test patterns for single stuck-at faults in combinational circuits. This new method generates test patterns in two steps: first, it constructs a formula expressing the Boolean difference between the unfaulted and faulted circuits, and second, it applies a Boolean satisfiability algorithm to the resulting formula. This approach differs from previous methods now in use, which search the circuit structure directly instead of constructing a formula from it. The new method is general and effective. It allows for the addition of heuristics used by structural search methods, and it has produced excellent results on popular test pattern generation benchmarks. >

Test pattern generation using Boolean satisfiability

This paper presents HITEC, a sequential circuit test generation package to generate test patterns for sequential circuits, without assuming the use of scan techniques or a reset state Several new techniques are introduced to improve the performance of test generation A targeted D element technique is presented, which greatly increases the number of possible mandatory assignments and reduces the over-specification of state variables which can sometimes result when using a standard PODEM algorithm A technique to use the state knowledge of previously generated vectors for state justification, without the memory overhead of a state transition diagram is presented For faults that were aborted during the standard test generation phase, knowledge that was gained about fault propagation, by the fault simulator, is used These techniques, when used together, produce the best published results for the ISCAS89 sequential benchmark circuits

HITEC: a test generation package for sequential circuits

VLSI Test Principles and Architectures: Design for Testability (Systems on Silicon)

An automatic test pattern generation system, SOCRATES, is presented. SOCRATES includes several novel concepts and techniques that significantly improve and accelerate the automatic test pattern generation process for combinational and scan-based circuits. Based on the FAN algorithm, improved implication, sensitization, and multiple backtrace procedures are described. The application of these techniques leads to a considerable reduction of the number of backtrackings and an earlier recognition of conflicts and redundancies. Several experiments using a set of combinational benchmark circuits demonstrate the efficiency of SOCRATES and its cost-effectiveness, even in a workstation environment. >

SOCRATES: a highly efficient automatic test pattern generation system

The authors present several concepts and techniques aiming at a further improvement and acceleration of the deterministic test-pattern-generation and redundancy identification process. In particular, they describe an improved implication procedure and an improved unique sensitization procedure. While the improved implication procedure takes advantage of the dynamic application of a learning procedure, the improved unique sensitization procedure profits from a dynamic and careful consideration of the existing situation of value assignments in the circuit. As a result of the application of the proposed techniques, SOCRATES is capable of both successfully generating a test pattern for all testable faults in a set of combinational benchmark circuits, and of identifying all redundant faults with less than ten backtrackings. >

M.H. Schulz

Papers

SOCRATES: a highly efficient automatic test pattern generation system

Improved deterministic test pattern generation with applications to redundancy identification