On Uniformly Sampling Traces of a Transition System

A key problem in constrained random verification (CRV) concerns generation of input stimuli that result in good coverage of the system's runs in targeted corners of its behavior space. Existing CRV solutions however provide no formal guarantees on the distribution of the system's runs. In this paper, we take a first step towards solving this problem. We present an algorithm based on Algebraic Decision Diagrams for sampling bounded traces (i.e. sequences of states) of a sequential circuit with provable uniformity (or bias) guarantees, while satisfying given constraints. We have implemented our algorithm in a tool called TraceSampler. Extensive experiments show that TraceSampler outperforms alternative approaches that provide similar uniformity guarantees.

[1]  Sasan Iman,et al.  The e Hardware Verification Language , 2004, Springer US.

[2]  Andreas Kuehlmann,et al.  Stimulus generation for constrained random simulation , 2007, 2007 IEEE/ACM International Conference on Computer-Aided Design.

[3]  Yehuda Naveh,et al.  Constraint-Based Random Stimuli Generation for Hardware Verification , 2006, AI Mag..

[4]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[5]  Supratik Chakraborty,et al.  A Scalable and Nearly Uniform Generator of SAT Witnesses , 2013, CAV.

[6]  Dimitris Achlioptas,et al.  Fast Sampling of Perfectly Uniform Satisfying Assignments , 2018, SAT.

[7]  Leonardo Mendonça de Moura,et al.  Generating efficient test sets with a model checker , 2004, Proceedings of the Second International Conference on Software Engineering and Formal Methods, 2004. SEFM 2004..

[8]  Harry D. Foster,et al.  Assertion-Based Design , 2010 .

[9]  Claude Castelluccia,et al.  Extending SAT Solvers to Cryptographic Problems , 2009, SAT.

[10]  Enrico Macii,et al.  Algebric Decision Diagrams and Their Applications , 1997, ICCAD '93.

[11]  Vu H. N. Phan,et al.  Weighted Model Counting with Algebraic Decision Diagrams , 2019 .

[12]  Supratik Chakraborty,et al.  Balancing scalability and uniformity in SAT witness generator , 2014, 2014 51st ACM/EDAC/IEEE Design Automation Conference (DAC).

[13]  Moshe Y. Vardi,et al.  ADDMC: Exact Weighted Model Counting with Algebraic Decision Diagrams , 2019, ArXiv.

[14]  Mihir Bellare,et al.  Uniform Generation of NP-Witnesses Using an NP-Oracle , 2000, Inf. Comput..

[15]  Olivier Coudert,et al.  Verifying Temporal Properties of Sequential Machines without Building Their State Diagrams , 1990, CAV.

[16]  Edmund M. Clarke,et al.  Symbolic model checking: 10/sup 20/ states and beyond , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[17]  Rahul Gupta,et al.  Knowledge Compilation meets Uniform Sampling , 2018, LPAR.

[18]  Michael Sipser,et al.  A complexity theoretic approach to randomness , 1983, STOC.

[19]  Héctor D. Menéndez,et al.  Output Sampling for Output Diversity in Automatic Unit Test Generation , 2022, IEEE Transactions on Software Engineering.

[20]  Rahul Gupta,et al.  WAPS: Weighted and Projected Sampling , 2019, TACAS.

[21]  Marcelo Arenas,et al.  Efficient Logspace Classes for Enumeration, Counting, and Uniform Generation , 2019, PODS.

[22]  Magdy S. Abadir,et al.  A Survey of Hybrid Techniques for Functional Verification , 2007, IEEE Design & Test of Computers.

[23]  Sanjit A. Seshia,et al.  On Parallel Scalable Uniform SAT Witness Generation , 2015, TACAS.

[24]  Wolfgang Roesner,et al.  Comprehensive Functional Verification: The Complete Industry Cycle , 2005 .

[25]  Leslie G. Valiant,et al.  Random Generation of Combinatorial Structures from a Uniform Distribution , 1986, Theor. Comput. Sci..

[26]  Edmund M. Clarke,et al.  Sequential circuit verification using symbolic model checking , 1991, DAC '90.

[27]  Harry Foster,et al.  Principles of verifiable RTL design , 2000 .

[28]  Larry J. Stockmeyer,et al.  The complexity of approximate counting , 1983, STOC.

[29]  Harry D. Foster.  Trends in functional verification: A 2014 industry study , 2015, 2015 52nd ACM/EDAC/IEEE Design Automation Conference (DAC).

[30]  Adnan Aziz,et al.  Constraint-based verification , 2006 .

[31]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..