Minimization of multiple-valued programmable logic array using simulated annealing. PDF
Preview Minimization of multiple-valued programmable logic array using simulated annealing.
NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS MINIMIZATION OF MULTIPLE-VALUED PROGRAMMABLE LOGIC ARRAY USING SIMULATED ANNEALING by Robert C.Earle December, 1991 Thesis Advisor: Jon T.Butler Approved for public release; distribution is unlimited T260062 SECURITYCLASSIFICATIONOFTHISPAGE REPORT DOCUMENTATION PAGE la REPORTSECURITYCLASSIFICATION 1b RESTRICTIVE MARKINGS Unclassified 2a SECURITYCLASSIFICATIONAUTHORITY 3 DISTRIBUTION/AVAILABILITYOFREPORT Approvedfor publicrelease;distributionisunlimited. 2b DECLASSIFICATION/DOWNGRADINGSCHEDULE 4.PERFORMINGORGANIZATIONREPORTNUMBER(S) 5.MONITORINGORGANIZATIONREPORT NUMBER(S) 6a NAMEOFPERFORMINGORGANIZATION 6b OFFICESYMBOL 7a NAMEOFMONITORINGORGANIZATION NavalPostgraduateSchool (Ifapplicable) NavalPostgraduateSchool 32 6c ADDRESS{City,State,andZIPCode) 7b ADDRESS(City, State,andZIPCode) Monterey,CA 93943-5000 Monterey,CA 93943 5000 8a NAMEOF FUNDING/SPONSORING 8b OFFICESYMBOL 9 PROCUREMENTINSTRUMENTIDENTIFICATION NUMBER ORGANIZATION (Ifapplicable) 8c ADDRESS(City,State,andZIPCode) 10 SOURCEOF FUNDINGNUMBERS ProgramLlemeniNo ProieclNo Taik No WorkUnaAccession Number 11.TITLE (IncludeSecurityClassification) MinimizationofMultiple-ValuedProgrammableLogicArrayUsingSimulatedAnnealing 12 PERSONALAUTHOR(S) Earle,RobertCharles 13a TYPEOFREPORT 13b TIMECOVERED 14 DATEOFREPORT(year,month,day) 15.PAGECOUNT Master'sThesis From To December 1991 67 16 SUPPLEMENTARY NOTATION TheviewsexpressedinthisthesisarethoseoftheauthoranddonotreflecttheofficialpolicyorpositionoftheDepartmentofDefenseortheU.S. Government. 17 COSATICODES 18 SUBJECTTERMS(continueonreverseifnecessaryandidentifybyblocknumber) FIELD GROUP SUBGROUP Multi-ValuedLogic; MinimizationHeuristics; PLADesign; SimulatedAnnealing 19 ABSTRACT(continueonreverseifnecessaryandidentifybyblocknumber) Guaranteedminimalrealizationsofmulti-valuedprogrammablelogicarrayscanonlybeaccomplishedbyanexhaustivesearch. Exhaustive searchisnotveryrealisticforcomplexexpressionsduetotheimmenseamountofCPUtimerequiredtoreachasolution. Tocircumvent thisproblem,heuristicshavebeendeveloped. Theyprovidenear-minimalsolutions,butusesubstantiallylessCPUtime. Thisthesis investigatesanewtypeofheuristicwhichisbuiltonthefoundationofsimpleimplicantoperationscontrolledbyanannealingprocess. This newtypeofheuristicissuperiortoexistingheuristicswithrespecttominimizationcapabilitybutrequiresmoreCPUtime. 20 DISTRIBUTION/AVAILABILITYOFABSTRACT 21 ABSTRACTSECURITYCLASSIFICATION Fl UNClASSlFICD/UNUMnEO J SAMtASREPORT ] OTICUSERS Unclassified 22a NAMEOF RESPONSIBLE INDIVIDUAL 22b TELEPHONE(IncludeAreacode) 22c OFFICE SYMBOL Butler,JonT. 408 646 3299 EC/Bu DD FORM 1473. 84 MAR 83APReditionmaybeuseduntilexhausted SECURITYCLASSIFICATIONOFTHIS PAGE Allothereditionsureobsolete Unclassified Approved for public release; distribution is unlimited. Minimization ofMultiple-Valued Programmable Logic Array UsingSimulated Annealing by RobertC. Earle Lieutenant United States Navy , B.S., United States Naval Academy, 985 1 Submitted in partial fulfillment ofthe requirements for the degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL December 1991 ABSTRACT Guaranteedminimal realizationsofmulti-valuedprogrammablelogic arrays canonly be accomplished by an exhaustive search. Exhaustive search is not very realistic for complex expressions due to theimmense amount ofCPU timerequired to reach a solution. To circumvent this problem, heuristics have been developed. They provide near-rninirnal solutions, but use substantially less CPU time. This thesis investigates a new type of heuristic which is built on the foundation of simple implicant operations controlled by an annealing process. This new typeofheuristic is superior to existing heuristics with respect to minimization capability but requires more CPU time. ui . . 1 5/j5 TABLE OF CONTENTS I. INTRODUCTION 1 A BACKGROUND 1 B. NEW APPROACH 2 II. TWO NEW HEURISTICS 3 A. THE ANNEALING PROCESS 3 B. OPERATIONS 5 1 COMBINABILITY 5 2. ABSORBABILITY 6 3. DIVISION 7 ADJACENCY 4 . 8 5. CONSENSUS 10 6. RESHAPE n C. HEURISTIC MECHANICS 12 1 . CUT & COMBINE !2 2. RESHAPE 13 III. EXPERIMENTAL RESULTS 15 A. ANNEALING PROCESS 15 B. PARAMETER ANALYSIS 18 IV
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