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SAT-Based Group Method for Verification of Logical Descriptions with Functional Indeterminacy

SAT-Based Group Method for Verification of Logical Descriptions with Functional Indeterminacy. Dmitry Novikov, Ludmila Cheremisinova United Institute of Informatics Problems of NAS of Belarus EWDTS’09 September 18 – 21, 2009, Moscow, Russia. email: yakov_nov@tut.by. Task formulation.

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SAT-Based Group Method for Verification of Logical Descriptions with Functional Indeterminacy

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  1. SAT-Based Group Method for Verification of Logical Descriptions with Functional Indeterminacy Dmitry Novikov, Ludmila Cheremisinova United Institute of Informatics Problems of NAS of Belarus EWDTS’09 September 18 – 21, 2009, Moscow, Russia email: yakov_nov@tut.by

  2. Task formulation Checking whether a given system of partially defined Boolean functions is implemented by a given combinational circuit Data representation System of partially defined Boolean functions Combinational circuit consisting of gates AND, OR and NOT

  3. Typical task formulation of formal verification Comparing circuit = const 0?

  4. CNF encoding combinational circuit CNF encoding gates (Tseitin transformation) k-input AND: k-inputOR: Combinational circuit Conventional CNF of the circuit

  5. Consistent testing multiple‑output cubes CNFs of not implementating the multiple‑output cubes (cube-prohibitive CNFs) extended CNF Multiple-output cubes Conventional CNF of the circuit Checking satisfiability of theextended CNF If the extended CNF is satisfiable the corresponding multiple‑output cube is not implemented by the circuit and implemented otherwise nsatisfiabilitychecks [CN08] L. Cheremisinova, D. Novikov, “SAT-Based Approach to Verification of Logical Descriptions with Functional Indeterminacy”, 8th International Workshop on Boolean Problems, Freiberg: September 18–19, 2008 5

  6. Simultaneoustesting multiple‑output cubes Multiple-output cubes Cube-prohibitive CNFs Prohibitive CNF extended CNF Conventional CNF of the circuit Prohibitive CNF To convert this formula toa CNF an encoding multiple‑output cubes is used Checking satisfiability of theextended CNF If the extended CNF is satisfiable at least one multiple‑output cube is not implemented by the circuit. 1 satisfiabilitycheck [CN08] 6

  7. Comparingsimultaneousand consistent testing The both methods have been implemented on C++ programming language and were compared. To check satisfiability CNFs we used SAT-solver MiniSat Time for checking satisfiability CNFs only Overall time for verification Preparing CNFs is time consuming! 7

  8. Grouptesting multiple‑output cubes Group-prohibitive CNFs Group-prohibitive CNF 1 Multiple-output cubes extended CNF Conventional CNF of the circuit Group-prohibitive CNF 2 Group-prohibitive CNF Checking satisfiability of theextended CNF If the extended CNF is satisfiable at least one multiple‑output cube from the corresponding group is not implemented by the circuit. n/rsatisfiabilitychecks, where r – size of groups, r = 200 8

  9. Experimental results fixed parameters : – the number Nv = 20 of input variables; – the number Nf = 20 of functions; – the number Nc = 500 of multiple‑output cubes; – the number Ng = 780 of network gates; – the average number Ni = 12,5 of gate inputs. (r – size of groups) Run times depending on Nv Run times depending on Nf (ropt – optimal size of groups) Run times depending on Nc Run times depending on Ng advantage: 34% 9

  10. Conclusion • A method for solving the task of checking whether a system of partially defined Boolean functions is implemented by a combinational circuit is proposed. • The suggested method is based on splitting the set of multiple‑output cubes into groups andchecking out satisfiability of the constructed extended conventional CNFs. • The method is meant to verify big systems of partiallydefined Boolean functions represented by sets of multi-output cubes having the small numbers of literals.

  11. Thank you for your attention email: yakov_nov@tut.by

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