Certified Context-Free Parsing: A formalisation of Valiant's Algorithm in Agda

Valiant (1975) has developed an algorithm for recognition of context free languages. As of today, it remains the algorithm with the best asymptotic complexity for this purpose. In this paper, we present an algebraic specification, implementation, and proof of correctness of a generalisation of Valiant's algorithm. The generalisation can be used for recognition, parsing or generic calculation of the transitive closure of upper triangular matrices. The proof is certified by the Agda proof assistant. The certification is representative of state-of-the-art methods for specification and proofs in proof assistants based on type-theory. As such, this paper can be read as a tutorial for the Agda system

Ten Digit Algorithms

This paper was presented as the A R Mitchell Lecture at the 2005 Dundee Biennial Conference on Numerical Analysis, 27 June 2005

Synthesizing Finite-state Protocols from Scenarios and Requirements

Scenarios, or Message Sequence Charts, offer an intuitive way of describing the desired behaviors of a distributed protocol. In this paper we propose a new way of specifying finite-state protocols using scenarios: we show that it is possible to automatically derive a distributed implementation from a set of scenarios augmented with a set of safety and liveness requirements, provided the given scenarios adequately \emph{cover} all the states of the desired implementation. We first derive incomplete state machines from the given scenarios, and then synthesis corresponds to completing the transition relation of individual processes so that the global product meets the specified requirements. This completion problem, in general, has the same complexity, PSPACE, as the verification problem, but unlike the verification problem, is NP-complete for a constant number of processes. We present two algorithms for solving the completion problem, one based on a heuristic search in the space of possible completions and one based on OBDD-based symbolic fixpoint computation. We evaluate the proposed methodology for protocol specification and the effectiveness of the synthesis algorithms using the classical alternating-bit protocol.Comment: This is the working draft of a paper currently in submission. (February 10, 2014

On Deciding Local Theory Extensions via E-matching

Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently encountered is that verification problems are often not fully expressible in the theories supported natively by the solvers. Many solvers allow the specification of application-specific theories as quantified axioms, but their handling is incomplete outside of narrow special cases. In this work, we show how SMT solvers can be used to obtain complete decision procedures for local theory extensions, an important class of theories that are decidable using finite instantiation of axioms. We present an algorithm that uses E-matching to generate instances incrementally during the search, significantly reducing the number of generated instances compared to eager instantiation strategies. We have used two SMT solvers to implement this algorithm and conducted an extensive experimental evaluation on benchmarks derived from verification conditions for heap-manipulating programs. We believe that our results are of interest to both the users of SMT solvers as well as their developers

The knowledge-based software assistant

Where the Knowledge Based Software Assistant (KBSA) is now, four years after the initial report, is discussed. Also described is what the Rome Air Development Center expects at the end of the first contract iteration. What the second and third contract iterations will look like are characterized