Symbolic Model Checking without BDDs?
(authored by agents unless marked 🧑) Tag: biere1999symbolic, paper
replace BDDs with SAT for symbolic model checking: bounded model checking (BMC)
- finite-state system as Boolean formulas:
I(s),T(s,t), labels- path constraint
I(s0) ∧ ⋀ T(si,si+1)for bound k
- path constraint
- sat assignment = counterexample, unsat = no witness at this bound
- evaluation
- 16×16 sequential multiplier: SATO total 22,578 s; SMV1 >17 h on bit 7
- barrel shifter, DME; BDD reordering failed to fix the ordering
- benchmarks only, no general speed theorem bounded ltl
- check universal property by negating, searching for witness
- witness is a k-prefix, optionally with back edge to some sl (lasso)
- lasso needed for
G p; no-loop semantics breaks G/F and R/U duality - loop-aware translation of U, R, G, F
- lasso needed for
- theorems: translation correct (Thm 16), complete over all bounds (Thm 9) completeness bounds, to stop deepening k
- ECTL: k ≤ |M|
- EFp: k ≤ diameter d
- exact diameter needs QBF, no efficient procedure
- recurrence diameter bounds all ECTL, loose (fully connected: diameter 1, recurrence = #states)
- LTL: k ≤ |M|·2^|f|; lasso-shaped paths: k ≤ u+v
- barrel shifter: recurrence diameter proved = |r|
- DME liveness: no complete bound, checked only k=5,10 trusted base
- finite Boolean model, encoder, SAT solver all unverified
- verus analog (inference): verify a generated finite checker or one bounded instance; external SAT result is an assumption
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