Sigma*: Symbolic Learning of Stream Filters

Matko Botincan, Domagoj Babic
University of Cambridge
University of Cambridge, 2012


   title={Sigma*: Symbolic Learning of Stream Filters},

   author={Botincan, M. and Babic, D.},



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We present Sigma*, a novel technique for learning symbolic models of software behavior. Sigma* addresses the challenge of synthesizing models of software by using symbolic conjectures and abstraction. By combining dynamic symbolic execution to discover symbolic input-output steps of the programs and counterexample guided abstraction refinement to over-approximate program behavior, Sigma* transforms arbitrary source representation of programs into faithful input-output models. We define a class of stream filters-programs that process streams of data items-for which Sigma* converges to a complete model if abstraction refinement eventually builds up a sufficiently strong abstraction. In other words, Sigma* is complete relative to abstraction. To represent inferred symbolic models, we use a variant of symbolic transducers that can be effectively composed and equivalence checked. Thus, Sigma* enables fully automatic analysis of behavioral properties such as commutativity, reversibility and idempotence, which is useful for web sanitizer verification and stream programs compiler optimizations, as we show experimentally. We also show how models inferred by Sigma* can be used to boost performance of stream programs through parallelized code generation.
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