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53
Indexed Predicate Discovery for Unbounded System Verification
 IN CAV’04
, 2004
"... Predicate abstraction has been proved effective for verifying several infinitestate systems. In predicate abstraction, an abstract system is automatically constructed given a set of predicates. Predicate abstraction coupled with automatic predicate discovery provides for a completely automatic v ..."
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Cited by 46 (6 self)
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Predicate abstraction has been proved effective for verifying several infinitestate systems. In predicate abstraction, an abstract system is automatically constructed given a set of predicates. Predicate abstraction coupled with automatic predicate discovery provides for a completely automatic verification scheme. For systems with unbounded integer state variables (e.g. software), counterexample guided predicate discovery has been successful in identifying the necessary predicates. For
Certifying Model Checkers
 In 13th International Conference Computer Aided Verification
, 2001
"... Model Checking is an algorithmic technique to determine whether a temporal property holds of a program. For linear time properties, a model checker produces a counterexample computation if the check fails. This computation acts as a "certificate" of failure, as it can be checked easily and indep ..."
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Cited by 34 (1 self)
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Model Checking is an algorithmic technique to determine whether a temporal property holds of a program. For linear time properties, a model checker produces a counterexample computation if the check fails. This computation acts as a "certificate" of failure, as it can be checked easily and independently of the model checker by simulating it on the program. On the other hand, no such certificate is produced if the check succeeds. In this paper, we show how this asymmetry can be eliminated with a certifying model checker. The key idea is that, with some extra bookkeeping, a model checker can produce a deductive proof on either success or failure. This proof acts as a certificate of the result, as it can be checked mechanically by simple, nonfixpoint methods that are independent of the model checker. We develop a deductive proof system for verifying branching time properties expressed in the mucalculus, and show how to generate a proof in this system from a model checking run. Proofs for linear time properties form a special case. A model checker that generates proofs can be used for many interesting applications, such as better ways of exploring errors in a program, and a tight integration of model checking with automated theorem proving. 1
Environment abstraction for parameterized verification
 In 7 th VMCAI, LNCS 3855
, 2006
"... Abstract. Many aspects of computer systems are naturally modeled as parameterized systems which renders their automatic verification difficult. In wellknown examples such as cache coherence protocols and mutual exclusion protocols, the unbounded parameter is the number of concurrent processes which ..."
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Cited by 19 (1 self)
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Abstract. Many aspects of computer systems are naturally modeled as parameterized systems which renders their automatic verification difficult. In wellknown examples such as cache coherence protocols and mutual exclusion protocols, the unbounded parameter is the number of concurrent processes which run the same distributed algorithm. In this paper, we introduce environment abstraction as a tool for the verification of such concurrent parameterized systems. Environment abstraction enriches predicate abstraction by ideas from counter abstraction; it enables us to reduce concurrent parameterized systems with unbounded variables to precise abstract finite state transition systems which can be verified by a finite state model checker. We demonstrate the feasibility of our approach by verifying the safety and liveness properties of Lamport’s bakery algorithm and Szymanski’s mutual exclusion algorithm. To the best of our knowledge, this is the first time both safety and liveness properties of the bakery algorithm have been verified at this level of automation. 1
Proving ptolemy right: The environment abstraction framework for model checking concurrent systems
 In TACAS
, 2008
"... Abstract. The parameterized verification of concurrent algorithms and protocols has been addressed by a variety of recent methods. Experience shows that there is a tradeoff between techniques which are widely applicable but depend on nontrivial human guidance, and fully automated approaches which a ..."
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Cited by 19 (2 self)
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Abstract. The parameterized verification of concurrent algorithms and protocols has been addressed by a variety of recent methods. Experience shows that there is a tradeoff between techniques which are widely applicable but depend on nontrivial human guidance, and fully automated approaches which are tailored for narrow classes of applications. In this spectrum, we propose a new framework based on environment abstraction which exhibits a large degree of automation and can be easily adjusted to different fields of application. Our approach is based on two insights: First, we argue that natural abstractions for concurrent software are derived from the “Ptolemaic ” perspective of a human engineer who focuses on a single reference process. For this class of abstractions, we demonstrate soundness of abstraction under very general assumptions. Second, most protocols in given a class of protocols – for instance, cache coherence protocols and mutual exclusion protocols – can be modeled by small sets of high level compound statements. These two insights allow to us efficiently build precise abstract models for given protocols which can then be model checked. We demonstrate the power of our method by applying it to various well known classes of protocols. 1
Complete instantiation for quantified formulas in Satisfiabiliby Modulo Theories
"... Abstract. Quantifier reasoning in Satisfiability Modulo Theories (SMT) is a longstanding challenge. The practical method employed in modern SMT solvers is to instantiate quantified formulas based on heuristics, which is not refutationally complete even for pure firstorder logic. We present several ..."
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Cited by 18 (1 self)
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Abstract. Quantifier reasoning in Satisfiability Modulo Theories (SMT) is a longstanding challenge. The practical method employed in modern SMT solvers is to instantiate quantified formulas based on heuristics, which is not refutationally complete even for pure firstorder logic. We present several decidable fragments of first order logic modulo theories. We show how to construct models for satisfiable formulas in these fragments. For richer undecidable fragments, we discuss conditions under which our procedure is refutationally complete. We also describe useful heuristics based on model checking for prioritizing or avoiding instantiations. 1
Liveness with Invisible Ranking
 SOFTWARE TOOLS FOR TECHNOLOGY TRANSFER
, 2006
"... The method of Invisible Invariants was developed originally in order to verify safety properties of parameterized systems in a fully automatic manner. The method is based on (1) a project&generalize heuristic to generate auxiliary constructs for parameterized systems, and (2) a small model theorem i ..."
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Cited by 16 (5 self)
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The method of Invisible Invariants was developed originally in order to verify safety properties of parameterized systems in a fully automatic manner. The method is based on (1) a project&generalize heuristic to generate auxiliary constructs for parameterized systems, and (2) a small model theorem implying that it is sufficient to check the validity of logical assertions of certain syntactic form on small instantiations of a parameterized system. The approach can be generalized to any deductive proof rule that (1) requires auxiliary constructs that can be generated by project&generalize, and (2) the premises resulting when using the constructs are of the form covered by the small model theorem. The method of invisible ranking, presented here, generalizes the approach to liveness properties of parameterized systems. Starting with a proof rule and cases where the method can be applied almost “as is,” the paper progresses to develop deductive proof rules for liveness and extend the small model theorem to cover many intricate families of parameterized systems.
What else is decidable about integer arrays?
"... Abstract. We introduce a new decidable logic for reasoning about infinite arrays of integers. The logic is in the ∃ ∗ ∀ ∗ firstorder fragment and allows (1) Presburger constraints on existentially quantified variables, (2) difference constraints as well as periodicity constraints on universally ..."
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Cited by 14 (1 self)
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Abstract. We introduce a new decidable logic for reasoning about infinite arrays of integers. The logic is in the ∃ ∗ ∀ ∗ firstorder fragment and allows (1) Presburger constraints on existentially quantified variables, (2) difference constraints as well as periodicity constraints on universally quantified indices, and (3) difference constraints on values. In particular, using our logic, one can express constraints on consecutive elements of arrays (e.g. ∀i. 0 ≤ i < n → a[i+1] = a[i]−1) as well as periodic facts (e.g. ∀i. i ≡2 0 → a[i] = 0). The decision procedure follows the automatatheoretic approach: we translate formulae into a special class of Büchi counter automata such that any model of a formula corresponds to an accepting run of the automaton, and vice versa. The emptiness problem for this class of counter automata is shown to be decidable, as a consequence of earlier results on counter automata with a flat control structure and transitions based on difference constraints. We show interesting program properties expressible in our logic, and give an example of invariant verification for programs that handle integer arrays. 1
Rapid Parameterized Model Checking of Snoopy Cache Coherence Protocols
 In 9th International Conference on Tools and Algorithms for Construction and Analysis of Systems (TACAS
, 2003
"... Abstract. A new method is proposed for parameterized reasoning about snoopy cache coherence protocols. The method is distinctive for being exact (sound and complete), fully automatic (algorithmic), and tractably efficient. The states of most cache coherence protocols can be organized into a hierarch ..."
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Cited by 13 (2 self)
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Abstract. A new method is proposed for parameterized reasoning about snoopy cache coherence protocols. The method is distinctive for being exact (sound and complete), fully automatic (algorithmic), and tractably efficient. The states of most cache coherence protocols can be organized into a hierarchy reflecting how tightly a memory block in a given cache state is bound to the processor. A broad framework encompassing snoopy cache coherence protocols is proposed where the hierarchy implicit in the design of protocols is captured as a preorder. This history graph where a global concrete state is represented by an abstract state reflecting the occupied local states. The abstract graph also takes into account the history of local transitions of the protocol that were fired along the computation to get to the global state. This permits the abstract history graph to exactly capture the behaviour of systems with an arbitrary number of homogeneous processes. Although the worst case size of the abstract history graph can be exponential in the size of the transition diagram describing the protocol, the actual size of the abstract history graph is small for standard cache protocols. The method is applicable to all 8 of the most common snoopy cache protocols described in Handy’s book [19] from IllinoisMESI to Dragon. The experimental results for parameterized verification of each of those 8 protocols document the efficiency of this new method in practice, with each protocol being verified in just a fraction of a second. It is emphasized that this is parameterized verification. 1
A generic framework for reasoning about dynamic networks of infinitestate processes
 In TACAS’07, volume 4424 of Lecture Notes in Computer Science
, 2007
"... Abstract. We propose a framework for reasoning about unbounded dynamic networks of infinitestate processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over so ..."
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Cited by 12 (1 self)
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Abstract. We propose a framework for reasoning about unbounded dynamic networks of infinitestate processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over some potentially infinite data domain such as integers, reals, etc. Furthermore, we define a logic, called CML (colored markings logic), for the description of CPN configurations. CML is a firstorder logic over tokens allowing to reason about their locations and their colors. Both CPNs and CML are parametrized by a color logic allowing to express constraints on the colors (data) associated with tokens. We investigate the decidability of the satisfiability problem of CML and its applications in the verification of CPNs. We identify a fragment of CML for which the satisfiability problem is decidable (whenever it is the case for the underlying color logic), and which is closed under the computations of post and pre images for CPNs. These results can be used for several kinds of analysis such as invariance checking, prepost condition reasoning, and bounded reachability analysis. 1.