Property Directed Reachability (PDR) Using Cubes of Non-state Variables With Property Directed Reachability Using Cubes of Non-state Variables With Property Directed Reachability PDR is a symbolic model checking algorithm for verifying safety properties. Ternary Valued Simulation With Gate Variables Shifting Time Frames A new SAT-Based algorithm for symbolic model checking has been gaining popularity. This algorithm, referred to as “Incremental Construction of Inductive Clauses for Indubitable Correctness” (IC3) or “Property Directed Reachability” (PDR), uses information learned from SAT instances of isolated time frames to either prove that an invariant exists, or provide a counter example. The information learned between each time frame is recorded in the form of cubes of the state variables. In this work, we study the effect of extending PDR to use cubes of intermediate variables representing the logic gates in the transition relation. We demonstrate that we can improve the runtime for satisfiable benchmarks by up to 3.2X, with an average speedup of 1.23X. Our approach also provides a speedup of up to 3.84X for unsatisfiable benchmarks. Ph.D. Candidate, University of Minnesota Associate Professor, University of Minnesota John Backes Marc Riedel Abstract SAT Results The algorithm solves SAT instances representing discrete time frames in isolation. Variables, Notation and Terms:Trace Properties BenchmarkTime States (s)Frames StatesInv. StatesTime Gates (s)Frames GatesInv. GatesTime Ratio 6s s s bj08amba2g3f bjrb07amba10andenv bjrb07amba3andenv bjrb07amba4andenv bjrb07amba5andenv bjrb07amba6andenv bjrb07amba7andenv bjrb07amba9andenv bob bobcohdoptdcd bobsmi2c cmudme cmudme eijkbs eijks eijks eijks eijks intel intel intel intel intel intel intel intel intel nusmvguidancep nusmvguidancep nusmvguidancep nusmvguidancep nusmvreactorp nusmvreactorp pdtpmscoherence pdtpmsheap pdtpmsretherrtf pdtpmsvsar pdtswvibs8x8p pdtswvqis10x6p pdtswvqis8x8p pdtswvroz10x6p pdtswvroz10x6p pdtswvroz8x8p pdtswvroz8x8p pdtswvsam6x8p pdtswvtma6x4p pdtswvtma6x4p pdtswvtma6x6p pdtswvtma6x6p pdtswvtms10x8p pdtswvtms12x8p pdtswvtms14x8p pdtvisbakery pdtvisbakery pdtvisbakery pdtvisgoodbakery pdtvisgoodbakery pdtvisgoodbakery pdtvisns3p pdtvisns3p pdtvisns3p pdtvisns3p pdtvisns3p pdtvisns3p pdtvisns3p pdtvisns3p pdtvistimeout pdtvisrethersqo pdtvisvending Geometric Average BenchmarkTime States(s)Frames StatesTime Gates (s)Frames GatesTime Ratio abp4p2ff abp4ptimoneg bc57sensorsp bc57sensorsp0neg bc57sensorsp bc57sensorsp1neg bc57sensorsp bc57sensorsp2neg bc57sensorsp intel intel intel intel irstdme irstdme irstdme nusmvtcasp5n nusmvtcastp prodcellp0neg prodcellp prodcellp1neg prodcellp prodcellp2neg prodcellp prodcellp prodcellp4neg Geometric Average Generally better results for satisfiable benchmarks Some unsatisfiable benchmarks proved faster Blocking Phase: Propagation Phase: Why Use Cubes of Gate Variables? x 0,x 1,x 2,x 3 g 0,g 1 x4x Three cubes in terms of x 0,x 1,x 2,x 3 can by blocked by one cube in terms of g 0,g 1 ! UNSAT Results Experiment Original Transition RelationNew Transition Relation Gates g 0,g 1,g 2,g 3 have only state variables in their cone of influence (COI)