Reference. SAT-Based Model Checking without Unrolling
A new form of SAT-based symbolic model checking is described. Instead of unrolling the transition relation, it incrementally generates clauses that are inductive relative to (and augment) stepwise approximate reachability information. In this way, the algorithm gradually refines the property, eventually producing either an inductive strengthening of the property or a counterexample trace. Our experimental studies show that induction is a powerful tool for generalizing the unreachability of given error states: it can refine away many states at once, and it is effective at focusing the proof search on aspects of the transition system relevant to the property. Furthermore, the incremental structure of the algorithm lends itself to a parallel implementation.
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Regularity and Quantification: A New Approach to Verify Distributed Protocols goelRegularityQuantificationNew
Proving that an unbounded distributed protocol satisfies a given safety property amounts to finding a quantified inductive invariant that implies the property for all possible instance sizes of the protocol. Existing methods for solving this problem can be described as search procedures for an invariant whose quantification prefix fits a particular template. We propose an alternative constructive approach that does not prescribe, a priori, a specific quantifier prefix. Instead, the required prefix is automatically inferred without any enumerative search by carefully analyzing the spatial and temporal regularity of the protocol. The key insight underlying this approach is that structural regularity and quantification are closely related concepts that express protocol invariance under different re-arrangements of its components and its unbounded evolution over time. We extended the finite-domain IC3/PDR algorithm to use these regularities and boost clause learning to automatically derive the required quantified inductive invariant by exploiting the connection between structural regularities and quantification. We also describe a procedure to automatically find a minimal finite size, the cutoff, that yields a quantified invariant proving safety for any size. Our approach is implemented in IC3PO, a new verifier for distributed protocols that significantly outperforms the state-of-the-art, scales orders of magnitude faster, and robustly derives compact inductive invariants fully automatically.
Sift: Using Refinement-guided Automation to Verify Complex Distributed Systems maSiftUsingRefinementguided
Distributed systems are hard to design and implement correctly. Recent work has tried to use formal verification techniques to provide rigorous correctness guarantees. These works present a hard choice, though. One must either opt for the power of refinement-based approaches like IronFleet and Verdi, at the cost of large amounts of manual effort; or choose the more automated approach of I4, IC3PO, SWISS and DistAI which give up the ability to prove refinement and the power and scalability that come with it.
On Symmetry and Quantification: A New Approach to Verify Distributed Protocols goelSymmetryQuantificationNew2021
Proving that an unbounded distributed protocol satisfies a given safety property amounts to finding a quantified inductive invariant that implies the property for all possible instance sizes of the protocol. Existing methods for solving this problem can be described as search procedures for an invariant whose quantification prefix fits a particular template. We propose an alternative constructive approach that does not prescribe, a priori, a specific quantifier prefix. Instead, the required prefix is automatically inferred without any search by carefully analyzing the structural symmetries of the protocol. The key insight underlying this approach is that symmetry and quantification are closely related concepts that express protocol invariance under different re-arrangements of its components. We propose symmetric incremental induction, an extension of the finite-domain IC3/PDR algorithm, that automatically derives the required quantified inductive invariant by exploiting the connection between symmetry and quantification. While various attempts have been made to exploit symmetry in verification applications, to our knowledge, this is the first demonstration of a direct link between symmetry and quantification in the context of clause learning during incremental induction. We also describe a procedure to automatically find a minimal finite size, the cutoff, that yields a quantified invariant proving safety for any size. Our approach is implemented in IC3PO, a new verifier for distributed protocols that significantly outperforms the state-of-the-art, scales orders of magnitude faster, and robustly derives compact inductive invariants fully automatically.
Finding Invariants of Distributed Systems: It’s a Small (Enough) World After All hanceFindingInvariantsDistributed
Today’s distributed systems are increasingly complex, leading to subtle bugs that are difficult to detect with standard testing methods. Formal verification can provably rule out such bugs, but historically it has been excessively labor intensive. For distributed systems, recent work shows that, given a correct inductive invariant, nearly all other proof work can be automated; however, the construction of such invariants is still a difficult manual task. In this paper, we demonstrate a new methodology for automating the construction of inductive invariants, given as input a (formal) description of the distributed system and a desired safety condition. Our system performs an exhaustive search within a given space of candidate invariants in order to find and verify inductive invariants which suffice to prove the safety condition. Central to our ability to search efficiently is our algorithm’s ability to learn from counterexamples whenever a candidate fails to be invariant, allowing us to check the remaining candidates more efficiently. We hypothesize that many distributed systems, even complex ones, may have concise invariants that make this approach practical, and in support of this, we show that our system is able to identify and verify inductive invariants for the Paxos protocol, which proved too complex for previous work.
AVR: Abstractly Verifying Reachability goelAVRAbstractlyVerifying2020
We present AVR, a push-button model checker for verifying state transition systems directly at the source-code level. AVR uses information embedded in the word-level syntax of the design representation to automatically perform scalable model checking by combining a novel syntax-guided abstraction-refinement technique with a word-level implementation of the IC3 algorithm. AVR provides independently-verifiable certificates that offer provable assurance and are easy to relate to the word-level system. Moreover, proof certificates can be further used in innovative ways to extract key design information and are useful in a growing number of applications.
I4: Incremental inference of inductive invariants for verification of distributed protocols maI4IncrementalInference2019
Designing and implementing distributed systems correctly is a very challenging task. Recently, formal verification has been successfully used to prove the correctness of distributed systems. At the heart of formal verification lies a computerchecked proof with an inductive invariant. Finding this inductive invariant, however, is the most difficult part of the proof. Alas, current proof techniques require inductive invariants to be found manually—and painstakingly—by the developer. In this paper, we present a new approach, Incremental Inference of Inductive Invariants (I4), to automatically generate inductive invariants for distributed protocols. The essence of our idea is simple: the inductive invariant of a finite instance of the protocol can be used to infer a general inductive invariant for the infinite distributed protocol. In I4, we create a finite instance of the protocol; use a model checking tool to automatically derive the inductive invariant for this finite instance; and generalize this invariant to an inductive invariant for the infinite protocol. Our experiments show that I4 can prove the correctness of several distributed protocols like Chord, 2PC and Transaction Chains with little to no human effort.
Towards Automatic Inference of Inductive Invariants ma-2019-towards
Ivy: Safety verification by interactive generalization padonIvySafetyVerification
Despite several decades of research, the problem of formal verification of infinite-state systems has resisted effective automation. We describe a system — Ivy — for interactively verifying safety of infinite-state systems. Ivy’s key principle is that whenever verification fails, Ivy graphically displays a concrete counterexample to induction. The user then interactively guides generalization from this counterexample. This process continues until an inductive invariant is found. Ivy searches for universally quantified invariants, and uses a restricted modeling language. This ensures that all verification conditions can be checked algorithmically. All user interactions are performed using graphical models, easing the user’s task. We describe our initial experience with verifying several distributed protocols.
Decidability of inferring inductive invariants padonDecidabilityInferringInductive2016
Induction is a successful approach for verification of hardware and software systems. A common practice is to model a system using logical formulas, and then use a decision procedure to verify that some logical formula is an inductive safety invariant for the system. A key ingredient in this approach is coming up with the inductive invariant, which is known as invariant inference. This is a major difficulty, and it is often left for humans or addressed by sound but incomplete abstract interpretation. This paper is motivated by the problem of inductive invariants in shape analysis and in distributed protocols. This paper approaches the general problem of inferring first-order inductive invariants by restricting the language L of candidate invariants. Notice that the problem of invariant inference in a restricted language L differs from the safety problem, since a system may be safe and still not have any inductive invariant in L that proves safety. Clearly, if L is finite (and if testing an inductive invariant is decidable), then inferring invariants in L is decidable. This paper presents some interesting cases when inferring inductive invariants in L is decidable even when L is an infinite language of universal formulas. Decidability is obtained by restricting L and defining a suitable well-quasi-order on the state space. We also present some undecidability results that show that our restrictions are necessary. We further present a framework for systematically constructing infinite languages while keeping the invariant inference problem decidable. We illustrate our approach by showing the decidability of inferring invariants for programs manipulating linked-lists, and for distributed protocols.
Cites 25 works (0 here)
External (25)
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