EHSAT: An Efficient RTL Satisfiability Solver Using an Extended DPLL Procedure

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EHSAT An Efficient RTL Satisfiability Solver
Using an Extended DPLL Procedure

• Shujun Deng, Jinian Bian, Weimin WuXiaoqing
  Yang, Yanni Zhao
• Department of Computer Science and Technology
• Tsinghua University
• Beijing, China
• June 6, 2007

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Outline

• Introduction
• EHSAT
• Preliminaries
• Decision Strategy
• Constraint Propagation
• Conflict-based Learning
• Experimental Results
• Summary

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Introduction

• RTL verification
• Bugs focus on RTL
• Higher abstraction level
• Catching more bugs earlier in the design cycle
  takes precedence in industrial practice
• Avoiding state-explosion
• Formal verification
• Theorem proving Not fully automatic
• Model checking
• Based on BDD State explosion
• Based on SAT Frequently applied
• Our solution RTL model checking based on hybrid
  SATsolver which contains not only Boolean
  variables butalso word variables
• Higher abstraction level
• More efficient

State explosion
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Classic SAT algorithm

• DPLL Procedure
• status preprocess()
• if(status!UNKNOWN) return status
• while(1)
• decide_next_branch()
• while(1)
• status deduce()
• if (status CONFLICT)
• blevel analyze_conflict()
• if (blevel 0)
• return UNSATISFIABLE
• else backtrack(blevel)
• else if (status SATISFIABLE)
• return SATISFIABLE
• else
• break

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Hybrid SAT solving

• HSAT Fallah et al. (DAC98)
• 3-SAT LP
• LPSAT Zeng et al. (DATE01)
• LP
• RACE Iyer (ITC03)
• Word ATPG
• HDPLL Parthasarathy et al. (DAC04, DAC05)
• Structural SAT Bit-vector Arithmetic (DAC04)
• Structural SAT Predicate Learning (DAC05)
• SMT (Satisfiability Modulo Theory) Solvers
• Yices SRI International
• UCLID CMU
• EHSAT
• How to use efficient SAT solving techniques on
  RTL?
• VSIDS, Two-literal-watching, Conflict-based
  learning

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Outline

• Introduction
• EHSAT
• Preliminaries
• Decision Strategy
• Constraint Propagation
• Conflict-based Learning
• Experimental Results
• Summary

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Basic concepts

• Hybrid literal the positive or negative form of
  either a Boolean variable or a bit in word
  variable.
• Hybrid clause a logic disjunction of one or more
  hybrid literals.
• Hybrid SAT given a problem withsome constraints
  for Boolean andword variables, find an
  assignmentto these variables that makes the
  constraints hold!

out XOR(cmpe0, cmpe1)cmpe0 CMP3 (stato1,
"4")cmpe1 CMP3 (stato2, "4")stato1
MUXW3 (s1, " 4" , " 0 ")stato2 MUXW3 (s2,
" 4" , " 0 ") Solution out 1, cmpe0 1,
cmpe1 0, stato1 4, stato2 0, s1 0, s2 1
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Overview of EHSAT

• Branch-and-bound procedure
• An extended DPLL procedure
• Decisions
• VSIDS Heuristic
• Boolean variables
• Word variable bits
• Constraint propagation
• Hybrid two-literal-watching scheme
• Interval reasoning
• Learning strategy
• 1BUIP (First Bit Unique Implication Point)
  Learning

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EHSAT framework

• Extended DPLL procedure
• decide() decision making
• hcp() constraint propagation
• First_Bit_UIP() 1BUIP(First Bit Unique
  Implication Point) Learning
• backtrack() backtrack to a proposed level

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Decision making

• Variable State Independent Decaying Sum (VSIDS)
• Recent conflicted literals have higher priority
• Heuristic
• Priority
• Boolean variables on the interface
• Ordinary Boolean variables
• Word-level variable bits
• Implementation
• Counting appearance
• Short clause (two literals) 2
• Multiplexer, Comparators 2
• Others 1
• Two queues Boolean is prior to word

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Hybrid two-literal-watching scheme

• Like two-literal-watching scheme in zChaff
• But fitting for hybrid clause database

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Predicate-based interval reasoning

• Predicate-based interval reasoning
• If a predicate is
• c LT (X, Y)
• and c 1
• X 64, 255
• Y 0, 127
• Then the interval of X can be changed to64,
  126 and that of Y to 65, 127 usinginterval
  arithmetic operations

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A circuit and implication graph

• Initial Assignment h 1
• Implication graph(The process of constraint
  propagation)

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Conflict-based learning

• Find out the real reason of a conflict.
• 1BUIP Only the UIPs with bit implication
  (Boolean variable or bit implication for word
  variables) can be added to the learning clauses.
• The difference between 1BUIP and 1UIP is shown in
  the figure.
• The added clause in this example is
  h?f?c?F1?e?g

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Outline

• Introduction
• EHSAT
• Preliminaries
• Decision Strategy
• Constraint Propagation
• Conflict-based Learning
• Experimental Results
• Summary

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Experimental results of EHSAT
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Experimental result analysis

• EHSAT outperforms HDPLL one or two orders
• HDPLL only makes decisions on Boolean variables
  while EHSAT makes on both
• Constraint propagation in HDPLL is incomplete,
  and an Omega library which performs
  fourier-motzkin elimination is used to check the
  consistence
• Yices could only succeed on some small cases
• Ignoring constraint information in circuits
• The run-time for GLPK increases quicker than
  EHSAT
• Translating Boolean constraints to word-level
  increases complexity
• The comparison between EHSAT and EHSAT confirms
  that making decisions on all the variables using
  VSIDS strategy is more efficient than that only
  making decisions on ports for hybrid SAT solving

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Outline

• Introduction
• EHSAT
• Preliminaries
• Decision Strategy
• Constraint Propagation
• Conflict-based Learning
• Experimental Results
• Summary

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Summary

• Efficient SAT techniques can be tuned to RTL
• Decision making
• VSIDS
• Heuristic
• Constraint propagation
• Hybrid two-literal-watching
• Predicate-based interval reasoning
• Conflict-based learning strategies
• 1BUIP
• Further improvement
• Modeling issues