Using ACL2 to Verify Loop Pipelining in Behavioral Synthesis

Behavioral synthesis involves compiling an Electronic System-Level (ESL) design into its Register-Transfer Level (RTL) implementation. Loop pipelining is one of the most critical and complex transformations employed in behavioral synthesis. Certifying the loop pipelining algorithm is challenging because there is a huge semantic gap between the input sequential design and the output pipelined implementation making it infeasible to verify their equivalence with automated sequential equivalence checking techniques. We discuss our ongoing effort using ACL2 to certify loop pipelining transformation. The completion of the proof is work in progress. However, some of the insights developed so far may already be of value to the ACL2 community. In particular, we discuss the key invariant we formalized, which is very different from that used in most pipeline proofs. We discuss the needs for this invariant, its formalization in ACL2, and our envisioned proof using the invariant. We also discuss some trade-offs, challenges, and insights developed in course of the project.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking

The verification of quantitative aspects like performance and dependability by means of model checking has become an important and vivid area of research over the past decade.\ud \ud An important result of that research is the logic CSL (continuous stochastic logic) and its corresponding model checking algorithms. The evaluation of properties expressed in CSL makes it necessary to solve large systems of linear (differential) equations, usually by means of numerical analysis. Both the inherent time and space complexity of the numerical algorithms make it practically infeasible to model check systems with more than 100 million states, whereas realistic system models may have billions of states.\ud \ud To overcome this severe restriction, it is important to be able to replace the original state space with a probabilistically equivalent, but smaller one. The most prominent equivalence relation is bisimulation, for which also a stochastic variant exists (Markovian bisimulation). In many cases, this bisimulation allows for a substantial reduction of the state space size. But, these savings in space come at the cost of an increased time complexity. Therefore in this paper a new distributed signature-based algorithm for the computation of the bisimulation quotient of a given state space is introduced.\ud \ud To demonstrate the feasibility of our approach in both a sequential, and more important, in a distributed setting, we have performed a number of case studies

Advanced Probabilistic Couplings for Differential Privacy

Differential privacy is a promising formal approach to data privacy, which provides a quantitative bound on the privacy cost of an algorithm that operates on sensitive information. Several tools have been developed for the formal verification of differentially private algorithms, including program logics and type systems. However, these tools do not capture fundamental techniques that have emerged in recent years, and cannot be used for reasoning about cutting-edge differentially private algorithms. Existing techniques fail to handle three broad classes of algorithms: 1) algorithms where privacy depends accuracy guarantees, 2) algorithms that are analyzed with the advanced composition theorem, which shows slower growth in the privacy cost, 3) algorithms that interactively accept adaptive inputs. We address these limitations with a new formalism extending apRHL, a relational program logic that has been used for proving differential privacy of non-interactive algorithms, and incorporating aHL, a (non-relational) program logic for accuracy properties. We illustrate our approach through a single running example, which exemplifies the three classes of algorithms and explores new variants of the Sparse Vector technique, a well-studied algorithm from the privacy literature. We implement our logic in EasyCrypt, and formally verify privacy. We also introduce a novel coupling technique called \emph{optimal subset coupling} that may be of independent interest