Title page for ETD etd-08102010-204533

Type of Document Master's Thesis
Author Goel, Neha
Author's Email Address nehagoel@vt.edu
URN etd-08102010-204533
Title Mining Multinode Constraints and Complex Boolean Expressions for Sequential Equivalence Checking
Degree Master of Science
Department Electrical and Computer Engineering
Advisory Committee
Advisor Name Title
Hsiao, Michael S. Committee Chair
Abbott, A. Lynn Committee Member
Ramakrishnan, Naren Committee Member
  • Inductive invariants
  • Implications
  • Data Mining
  • Formal verification
  • Finite state machines
Date of Defense 2010-07-30
Availability unrestricted
Integrated circuit design has progressed significantly over the last few decades. This increasing complexity of hardware systems poses several challenges to the digital hardware verification. Functional verification has become the most expensive and time-consuming task in the overall product development cycle. Almost 70\% of the total verification time is being consumed by design verification and it is projected to worsen further. One of the reasons for this complexity is the synthesis and optimization (automated as well as manual) techniques used to improve performance, area, delay, and other measures have made the final implementation of the design very different from the golden (reference) model. Determining the functional correctness between the reference and implementation using exhaustive simulation can almost always be infeasible. An alternative approach is to prove that the optimized design is functionally equivalent to the reference model, which is known to be functionally correct. The most widely used formal method to perform this process is equivalence checking. The success of combinational equivalence checking (CEC) has contributed to aggressive combinational logic synthesis and optimizations for circuits with millions of logic gates. However, without powerful sequential equivalence checking (SEC) techniques, the potential and extent of sequential optimization is quite limited. In other words, the success of SEC can unleash a plethora of aggressive sequential optimizations that can take circuit design to the next level. Currently, SEC remains extremely difficult compared to CEC, due to the huge search space of the problem.

Sequential Equivalence Checking remains a challenging problem, in this thesis we address the problem using efficient learning techniques. The first approach is to mine missing multi-node patterns from the mining database, verify them and add those proved as true during the unbounded SEC framework. The second approach is to mine powerful and generalized Boolean relationships among flip-flops and internal signals in a sequential circuit using a data mining algorithm. In contrast to traditional learning methods, our mining algorithms can extract illegal state cubes and inductive invariants. These invariants can be arbitrary Boolean expressions and can help in pruning a large don't-care space for equivalence checking.

The two approaches are complementary to each other in nature. One computes the subset of illegal states that cannot occur in the normal function mode and the other approach mines legal constraints that represent the characteristics of the miter circuit and can never be violated. These powerful relations, when added as new constraint clauses to the original formula, help to significantly increase the deductive power for the SAT engine, thereby pruning a larger portion of the search space. Likewise, the memory required and time taken to solve the SEC problem is alleviated.

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