Software Verification with PDR: An Implementation of the State of the Art

Abstract

Property-directed reachability (PDR) is a SAT/SMT-based reachability algorithm that incrementally constructs inductive invariants. After it was successfully applied to hardware model checking, several adaptations to software model checking have been proposed. We contribute a replicable and thorough comparative evaluation of the state of the art: We (1) implemented a standalone PDR algorithm and, as improvement, a PDR-based auxiliary-invariant generator for k -induction, and (2) performed an experimental study on the largest publicly available benchmark set of C verification tasks, in which we explore the effectiveness and efficiency of software verification with PDR. The main contribution of our work is to establish a reproducible baseline for ongoing research in the area by providing a well-engineered reference implementation and an experimental evaluation of the existing techniques. 1 extern void __VERIFIER_error() __attribute__ ֒→ ((__noreturn__)); 2 extern unsigned int __VERIFIER_nondet_uint(void); 3 void __VERIFIER_assert(int cond) { 4 if (!(cond)) { 5 ERROR: __VERIFIER_error(); 6 } 7 return; 8 } 9 int main(void) { 10 unsigned int w = __VERIFIER_nondet_uint(); 11 unsigned int x = w; 12 unsigned int y = w + 1; 13 unsigned int z = x + 1; 14 while (__VERIFIER_nondet_uint()) { 15 y++; 16 z++; 17 } 18 __VERIFIER_assert(y == z);

Software model-checking as cyclic-proof search

“…Property-directed reachability (or PDR) refers to the IC3 algorithm [Bradley 2011;Een et al 2011] and its derivatives [Beyer and Dangl 2020;Birgmeier et al 2014;Cimatti and Griggio 2012;Cimatti et al 2014;Hoder and Bjùrner 2012;Komuravelli et al 2014Komuravelli et al , 2013. This section compares PDR and Impact/mc, in particular Impact/mc with IndPDR.…”

“…Unified framework. Beyer et al have been developing a configurable software model checker CPAchecker [Beyer et al 2007[Beyer et al , 2008Beyer and Keremoglu 2011], which implements various software model checking algorithms [Beyer and Dangl 2020;Beyer et al 2018;Beyer and Wendler 2012] in a unified framework in a configurable manner. Though our logical foundation also provides a unified framework, the level of abstraction is significantly different: we reconstruct well-known algorithms from a few simple and declarative principles, whereas CPAchecker achieves the reconstruction via modular design and implementation of software model checking components.…”

“…To address the so-called "state explosion problemž in model checking real-world programs, the past decades have witnessed a significant development of state-space abstraction and refinement techniques including predicate abstraction [Ball et al 2001;Graf and Saïdi 1997], CounterExample-Guided Abstraction Refinement (CEGAR) [Clarke et al 2003], lazy abstraction [Beyer and Wendler 2012;Henzinger et al 2004Henzinger et al , 2002McMillan 2006], and Property Directed Reachability (PDR) [Beyer and Dangl 2020;Birgmeier et al 2014;Bradley 2011;Cimatti and Griggio 2012;Cimatti et al 2014;Een et al 2011;Hoder and Bjùrner 2012;Komuravelli et al 2014Komuravelli et al , 2013Vizel and Gurfinkel 2014].…”

Software Model-Checking as Cyclic-Proof Search

“…Property-directed reachability (or PDR) refers to the IC3 algorithm [Bradley 2011;Een et al 2011] and its derivatives [Beyer and Dangl 2020;Birgmeier et al 2014;Cimatti and Griggio 2012;Cimatti et al 2014;Hoder and Bjørner 2012;Komuravelli et al 2014Komuravelli et al , 2013. This section compares PDR and Impact/mc, in particular Impact/mc with IndPDR.…”

“…To address the so-called "state explosion problem" in model checking real-world programs, the past decades have witnessed a significant development of state-space abstraction and refinement techniques including predicate abstraction [Ball et al 2001;Graf and Saïdi 1997], CounterExample-Guided Abstraction Refinement (CEGAR) [Clarke et al 2003], lazy abstraction [Beyer and Wendler 2012;Henzinger et al 2004Henzinger et al , 2002McMillan 2006], and Property Directed Reachability (PDR) [Beyer and Dangl 2020;Birgmeier et al 2014;Bradley 2011;Cimatti and Griggio 2012;Cimatti et al 2014;Een et al 2011;Hoder and Bjørner 2012;Komuravelli et al 2014Komuravelli et al , 2013Vizel and Gurfinkel 2014].…”