interpretation techniques prove properties of programs by computing abstract fixpoints. All such analyses suffer from the possibility of false errors. We present a new counterexample driven refinement technique to reduce false errors in abstract interpretations. Our technique keeps track of the precision losses during forward fixpoint computation, and does a precise backward propagation from the error to either confirm the error as a true error, or identify a refinement so as to avoid the false error. Our technique is quite simple, and is independent of the specific abstract domain used. An implementation of our technique for affine transition systems is able to prove invariants generated by the StInG tool [19] without doing any specialized analysis for linear relations. Thus, we hope that the technique can work for other abstract domains as well. We sketch how our technique can be used to perform shape analysis by simply defining an appropriate widening operator over shape graphs.

Abstract. Abstract interpretation techniques prove properties of programs by computing abstract fixpoints. All such analyses suffer from the possibility of false errors. We present three techniques to automatically refine such abstract interpretations to reduce false errors: (1) a new operator called interpolated widen, which automatically recovers precision lost due to widen, (2) a new way to handle disjunctions that arise due to refinement, and (3) a new refinement algorithm, which refines abstract interpretations that use the join operator to merge abstract states at join points. We have implemented our techniques in a tool Dagger. Our experimental results show our techniques are effective and that their combination is even more effective than any one of them in isolation. We also show that Dagger is able to prove properties of C programs that are beyond current abstraction-refinement tools, such as

This paper describes a precise numerical abstract domain for use in timing analysis. The numerical abstract domain is parameterized by a linear abstract domain and is constructed by means of two domain lifting operations. One domain lifting operation is based on the principle of expression abstraction (which involves defining a set of expressions and specifying their semantics using a collection of directed inference rules) and has a more general applicability. It lifts any given abstract domain to include reasoning about a given set of expressions whose semantics is abstracted using a set of axioms. The other domain lifting operation incorporates disjunctive reasoning into a given linear relational abstract domain via introduction of max expressions. We present experimental results demonstrating the potential of the new numerical abstract domain to discover a wide variety of timing bounds (including polynomial, disjunctive, logarithmic, exponential, etc.) for small C programs.

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In this article, we present a new shape analysis algorithm. The key distinguishing aspect of our algorithm is that it is completely compositional, bottom-up and noniterative. We present our algorithm as an inference system for computing Hoare triples summarizing heap manipulating programs. Our inference rules are compositional: Hoare triples for a compound statement are computed from the Hoare triples of its component statements. These inference rules are used as the basis for bottom-up shape analysis of programs.Specifically, we present a Logic of Iterated Separation Formulae (LISF), which uses the iterated separating conjunct of Reynolds [2002] to represent program states. A key ingredient of our inference rules is a strong bi-abduction operation between two logical formulas. We describe sound strong bi-abduction and satisfiability procedures for LISF.We have built a tool called SPINE that implements these inference rules and have evaluated it on standard shape analysis benchmark programs. Our experiments show that SPINE can generate expressive summaries, which are complete functional specifications in many cases.

We consider the problem if a given program satisfies a specified safety property. Interesting programs have infinite state spaces, with inputs ranging over infinite domains, and for these programs the property checking problem is undecidable. Two broad approaches to property checking are testing and verification. Testing tries to find inputs and executions which demonstrate violations of the property. Verification tries to construct a formal proof which shows that all executions of the program satisfy the property. Testing works best when errors are easy to find, but it is often difficult to achieve sufficient coverage for correct programs. On the other hand, verification methods are most successful when proofs are easy to find, but they are often inefficient at discovering errors. We propose a new algorithm, Synergy, which combines testing and verification. Synergy unifies several ideas from the literature, including counterexample-guided model checking, directed testing, and partition refinement. This paper presents a description of the Synergy algorithm, its theoretical properties, a comparison with related algorithms, and a prototype implementation called Yogi.

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We present the design, implementation, and evaluation of INSTalytics , a co-designed stack of a cluster file system and the compute layer, for efficient big-data analytics in large-scale data centers. INSTalytics amplifies the well-known benefits of data partitioning in analytics systems; instead of traditional partitioning on one dimension, INSTalytics enables data to be simultaneously partitioned on four different dimensions at the same storage cost, enabling a larger fraction of queries to benefit from partition filtering and joins without network shuffle. To achieve this, INSTalytics uses compute-awareness to customize the three-way replication that the cluster file system employs for availability. A new heterogeneous replication layout enables INSTalytics to preserve the same recovery cost and availability as traditional replication. INSTalytics also uses compute-awareness to expose a new sliced-read API that improves performance of joins by enabling multiple compute nodes to read slices of a data block efficiently via co-ordinated request scheduling and selective caching at the storage nodes. We have built a prototype implementation of INSTalytics in a production analytics stack, and we show that recovery performance and availability is similar to physical replication, while providing significant improvements in query performance, suggesting a new approach to designing cloud-scale big-data analytics systems.