DAG inlining: a decision procedure for reachability-modulo-theories in hierarchical programs

Abstract

A hierarchical program is one with multiple procedures but no loops or recursion. This paper studies the problem of deciding reachability queries in hierarchical programs where individual statements can be encoded in a decidable logic (say in SMT). This problem is fundamental to verification and most directly applicable to doing bounded reachability in programs, i.e., reachability under a bound on the number of loop iterations and recursive calls. The usual method of deciding reachability in hierarchical programs is to first inline all procedures and then do reachability on the resulting single-procedure program. Such inlining unfolds the call graph of the program to a tree and may lead to an exponential increase in the size of the program. We design and evaluate a method called DAG inlining that unfolds the call graph to a directed acyclic graph (DAG) instead of a tree by sharing the bodies of procedures at certain points during inlining. DAG inlining can produce much more compact representations than tree inlining. Empirically, we show that it leads to significant improvements in the running time of a state-of-the-art verifier.

Solving Constrained Horn Clauses Using Dependence-Disjoint Expansions

“…Given an arbitrary recursion-free CHC system S, SHARA reduces S to a CDD system S ′ and solves S ′ directly. In general, S ′ may have size exponential in the size of S. However, SHARA generates CDD systems via heuristics analogous to those used to generate compact verification conditions of hierarchical programs [6,14]. In practice these heuristics often yield CDD systems which are small with respect to the input system.…”

“…DAG inlining attempts to generate compact verification conditions for hierarchical programs [14]. SHARA attempts to solve recursion-free CHC systems by reducing them to compact CDD systems.…”

“…In particular, feasible variations of EXPAND can be generated from different implementations of SHAREDREL, each of which chooses clause-relation pairs to return based on different heuristics. We expect that other expansion algorithms can also be developed by generalizing algorithms introduced in previous work on generating compact verification conditions of hierarchical programs [14].…”

“…In the worst case, it is possible that the size of S ′ may be exponential in the size of S. However, empirically we have found that the size of S ′ is usually close enough to the size of S that SHARA frequently outperforms DUALITY, one of the best known CHC solvers. The procedure implemented in SHARA is a generalization of existing techniques that synthesize compact verification conditions for hierarchical programs [6,14]. Given a general (possibly recursive) CHC system, SHARA solves a sequence of recursion-free systems.…”

“…Recursion-free CHC systems are an important subclass for two reasons. First, recursion-free systems can be used to model safety properties for hierarchical programs [14,15] (programs with only bounded iteration and recursion). Second and most importantly, a well-known approach for solving a general CHC system reduces the input problem to solving a sequence of recursionfree systems.…”