: The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer aided design, computer aided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the satisfiability problems.

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Algorithms for the Satisfiability (SAT) Problem: A Survey,

Conventional logic synthesis systems are targeted towards reducing the area required by a logic block, as measured by the literal count or gate count; or, improving the performance in terms of gate delays; or, improving the testability of the synthesized circuit, as measured by the irredundancy of the resultant circuit. In this paper, we address the problem of developing reliability driven logic synthesis algorithms for multilevel logic circuits, which are integrated within the MIS synthesis system. Our procedures are based on concurrent error detection techniques that have been proposed in the past for two level circuits, and adapting those techniques to multilevel logic synthesis algorithms. Three schemes for concurrent error detection in a multilevel circuit are proposed in this paper, using which all the single stuck at faults in the circuit can be detected concurrently. The first scheme uses duplication of a given multilevel circuit with the addition of a totally self-checking comparator. The second scheme proposes a procedure to generate the multilevel circuit from a two level representation under some constraint such that, the Berger code of the output vector can be used to detect any single fault inside the circuit, except at the inputs. A constrained technology mapping procedure is also presented in this paper. The third scheme is based on parity codes on the outputs. The outputs are partitioned using a novel partitioning algorithm, and each partition is implemented using a multilevel circuit. Some additional parity coded outputs are generated. In all three schemes, all the necessary checkers are generated automatically and the whole circuit is placed and routed using the Timberwolf layout package. The area overheads for several benchmark examples are reported in this paper. The entire procedure is integrated into a new system called RSYN. >

RSYN: a system for automated synthesis of reliable multilevel circuits

This paper proposes a new approach to multi-level logic optimization based on ATPG (Automatic Test Pattern Generation). Previous ATPG-based methods for logic minimization suffered from the limitation that they were quite restricted in the set of possible circuit transformations. We show that the ATPG-based method presented here allows (in principle) the transformation of a given combinational network C into an arbitrary, structurally different but functionally equivalent combinational network C'. Furthermore, powerful heuristics are presented in order to decide what network manipulations are promising for minimizing the circuit. By identifying indirect implications between signals in the circuit, transformations can be derived which are “good” candidates for the minimization of the circuit. In particular, it is shown that Recursive Learning can derive “good” Boolean divisors justifying the effort to attempt a Boolean division. For 9 out of 10 ISCAS-85 benchmark circuits our tool HANNIBAL obtains smaller circuits than the well-known synthesis system SIS.

http://www.cecs.uci.edu/~papers/compendium94-03/papers/1994/iccad94/pdffiles/01a_2.pdf

Multi-level logic optimization by implication analysis

A new synthesis technique for designing finite state machines with on-line parity checking is presented. The output logic and the next-state logic of the finite state machines are checked independently. By checking parity on the present state instead of the next state, this technique allows detection of errors in bistable elements (that were hitherto not detected by many previous techniques) while requiring no changes in the original machine specifications. This paper also examines design choices with respect to parity prediction circuits. Two such examined choices are the multi-parity-group and the single-parity-group techniques. A new state encoding technique based on the JEDI program is developed for the synthesis of the next-state logic with an additional parity output. Synthesis results produced by our proposed procedure for the MCNC'89 FSM benchmark circuits show on average a 25% reduction in literal counts compared to previous techniques.

/pdf/finite-state-machine-synthesis-with-concurrent-error-59dcudl6pk.pdf

Finite state machine synthesis with concurrent error detection

It is shown that optimal sequential logic synthesis can produce irredundant, fully testable finite-state machines. Synthesizing a sequential circuit from a state transition graph description involves the steps of state minimization, state assignment, and logic optimization. Previous approaches to producing fully and easily testable sequential circuits have involved the use of extra logic and constraints on state assignments and logic optimization. Here it is shown that 100% testability can be ensured without the addition of extra logic and without constraints on the state assignment and logic optimization. Unlike previous synthesis approaches to ensuring fully testable machines, there is no area/performance penalty associated with this approach. This technique can be used in conjunction with previous approaches to ensure that the synthesized machine is easily testable. Given a state-transition-graph specification, a logic-level automaton that is fully testable for all single stuck-at faults in the combinational logic without access to the memory elements is synthesized. >

Irredundant sequential machines via optimal logic synthesis

The authors outline a synthesis procedure which beginning from a state transition graph (STG) description of a sequential machine produces an optimized fully and easily testable logic implementation. This logic-level implementation is guaranteed to be testable for all single stuck-at faults in the combinational logic and the test sequences for these faults can be obtained using combinational test generation techniques alone. The sequential machine is assumed to have a reset state and be R-reachable. All single stuck-at faults in the combinational logic and the input and output stuck-at faults of the memory elements in the synthesized logic-level automaton can be tested without access to the memory elements using these test sequences. Thus this procedure represents an alternative to a scan design methodology. The area penalty incurred due to the constraints on the optimization are small. The performance of the synthesized design is usually better than that of an unconstrained design optimized for area alone. The authors show that an intimate relationship exists between state assignment and the testability of a sequential machine. They propose a procedure of constrained state assignment and logic optimization which guarantees testability for both Moore and Mealy machines. >

A synthesis and optimization procedure for fully and easily testable sequential machines

An outline is presented of a synthesis procedure that, beginning from a state transition graph (STG) description of a sequential machine, produces an optimized easily testable programmable logic array (PLA) based logic implementation. Previous approaches to synthesizing easily testable sequential machines have concentrated on the stuck-at-fault model; for PLAs, an extended fault model called the crosspoint fault model has been used. The authors propose a procedure of constrained state assignment and logic optimization which guarantees testability for all combinationally irredundant crosspoint faults in a PLA-based finite-state machine. No direct access to the flip-flops is required. The test sequences to detect these faults can be obtained using combinational test generation techniques alone. This procedure thus represents an alternative to a scan design methodology. Results are presented which show that the area/performance penalties in return for easy testability are small. >

H.-K.T. Ma

Papers

A synthesis and optimization procedure for fully and easily testable sequential machines

Easily testable PLA-based finite state machines