BDD model checker: early variable quantification#1801
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Implement the early variable quantification optimisation from Burch, Clarke, McMillan, Dill, Hwang: "Symbolic Model Checking for Sequential Circuit Verification" (1992). Instead of building the monolithic conjunction of all transition conjuncts and then quantifying out next-state variables, we interleave conjunction and quantification: after conjoining each partition, we immediately quantify out next-state variables that do not appear in any remaining partition. This can reduce intermediate BDD sizes from exponential to polynomial. The old monolithic approach is retained as EX_monolithic for benchmarking purposes. A benchmark in benchmarking/bdd_model_checking/ demonstrates the effect using an identity relation with separated variable ordering, where the monolithic approach produces O(3^N) peak BDD nodes while early quantification stays O(1).
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Implement the early variable quantification optimisation from Burch, Clarke, McMillan, Dill, Hwang: Symbolic Model Checking for Sequential Circuit Verification (1992).
Changes
Instead of building the monolithic conjunction of all transition conjuncts and then quantifying out next-state variables,
EXnow interleaves conjunction and quantification: after conjoining each partition, it immediately quantifies out next-state variables that do not appear in any remaining partition. This can reduce intermediate BDD sizes from exponential to polynomial.The core addition is
project_next_early(), which:The old monolithic approach is retained as
EX_monolithic()for benchmarking.Benchmark
A benchmark in
benchmarking/bdd_model_checking/demonstrates the effect using an identity relation with separated variable ordering. The metric is peak intermediate BDD node count, which directly reflects memory usage.Monolithic peak BDD nodes grow as O(3^N); early quantification keeps them O(1). Time grows O(N) for early quantification vs exponentially for the monolithic approach.
Testing
All unit tests (122 assertions, 32 test cases) and all regression tests pass.