Introducing stateful conditional branching in Ciaramella

Conditional branching in Synchronous Data Flow (SDF) networks is a long-standing issue as it clashes with the underlying synchronicity model. For this reason, conditional update of state variables is rarely implemented in data flow programming environments, unlike simpler selection operators that do not execute code conditionally. We propose an extension to SDF theory to represent stateful conditional branching. We prove the effectiveness of such approach by adding conditional constructs to the Ciaramella programming language without compromising its modular declarative paradigm and maintaining domain-specific optimizations intact. This addition enables easy implementation of common DSP algorithms and helps in writing efficient complex programs

Polynomial Invariants for Affine Programs

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions). Our main tool is an algebraic result of independent interest: given a finite set of rational square matrices of the same dimension, we show how to compute the Zariski closure of the semigroup that they generate