Hardware Verification using Monadic Second-Order Logic

Abstract

We show how the second-order monadic theory of strings can be used to specify hardware components and their behavior. This logic admits a decision procedure and counter-model generator based on canonical automata for formulas. We have used a system implementing these concepts to verify, or find errors in, a number of circuits proposed in the literature. The techniques we use make it easier to identify regularity in circuits, including those that are parameterized or have parameterized behavioral specifications. Our proofs are semantic and do not require lemmas or induction as would be needed when employing a conventional theory of strings as a recursive data type.

Languages, Automata, and Logic

“…by an iterated exponential of the form 2^(2^: : : (2 n ) : : : ) in the length n of the given formula). It is remarkable, however, that a conversion algorithm has been implemented which a l l o ws nontrivial practical applications in hardware veri cation ( BK95]). …”

A domain-specific language for regular sets of strings and trees

“…The basic predicates are set membership t 2 T , equality t 1 = t 2 , ancestor relation t 1 t 2 , and set inclusion T 1 T 2 . The logic permits the usual connectives ^, _, : and rst and second-order quanti ers 8 1 , 9 1 , 8 2 , 9 2 . By convention, a leaf is a position p for which p = p:0 and p = p:1.…”

MONA Implementation Secrets

“…From the language point of view, M2L-Str corresponds exactly to the regular languages (all formulas correspond to automata and vice versa), and WS1S corresponds to those regular languages that are closed under concatenation by 0's. These properties make M2L-Str preferable for some applications [4,44]. However, the fact that not all positions have a successor often makes M2L-Str rather unnatural to use.…”

“…Happily, many interesting projects fit into this niche, including hardware verification [4,1], pointer analysis [23,17], controller synthesis [44,22], natural languages [39], parsing tools [14], software design descriptions [29], Presburger arithmetic [45], and verification of concurrent systems [32,31,24,42,46].…”