[Glean] State Explosion Problem and Formal Verification

Published: January 13, 2021 by SingularityKChen (Last updated: January 13, 2021 )

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• State Explosion Problem and Formal Verification

State Explosion Problem and Formal Verification¹

In a n-bit counter, the number of states of the counter is exponential in the number of bits, i.e., $2^n$. In model checking we refer to this problem as the state explosion problem. All model checkers suffer from it.

Solutions:

1. One of the first major advances was symbolic model checking with binary decision diagrams (BDDs). In this approach, a set of states is represented by a BDD instead of by listing each state individually. The BDD representation is often exponentially smaller in practice. Model checking with BDDs is performed using a fixed point algorithm.
2. Another major advance is the partial order reduction, which exploits the independence of actions in a system with asynchronous composition of processes.
3. A third major advance is counterexample-guided abstraction refinement, which adaptively tries to find an appropriate level refinement, precise enough to verify the property of interest yet not burdened with irrelevant detail that slows down verification.
4. Finally, bounded model checking exploits fast Boolean satisfiability (SAT) solvers to search for counterexamples of bounded length.

1. E. M. Clarke, W. Klieber, M. Nováček, and P. Zuliani, “Model Checking and the State Explosion Problem,” in Tools for Practical Software Verification, Sep. 2011, pp. 1–30, doi: 10.1007/978-3-642-35746-6_1. ↩ ↩