Technical Talk: Syntactic reasoning for digital circuits using graphs

Dan R. Ghica

When: Thursday, November 19, 10am (Edinburgh)

Abstract: I will present a general diagrammatic theory of digital circuits, based on connections between monoidal categories and graph rewriting. The main achievement of the paper is conceptual, filling a foundational gap in reasoning syntactically and symbolically about a large class of digital circuits (discrete values, discrete delays, feedback). This complements the dominant approach to circuit modelling, which relies on simulation. The main advantage of our symbolic approach is the enabling of automated reasoning about parameterized circuits, with a potentially interesting new application to partial evaluation of digital circuits. Relative to the recent interest and activity in categorical and diagrammatic methods, our work makes several new contributions. The most important is establishing that categories of digital circuits are Cartesian and admit, in the presence of feedback expressive iteration axioms. The second is producing a general yet simple graph-rewrite framework for reasoning about such categories in which the rewrite rules are computationally efficient, opening the way for practical applications.

Video: https://www.youtube.com/watch?v=90X2kyO88Tc 

Slides: Diagram circuits

References

• Dan R. Ghica, Achim Jung, Aliaume Lopez: Diagrammatic Semantics for Digital Circuits. CSL 2017: 24:1-24:16

• Dan  R. Ghica, Achim Jung: Categorical semantics of digital circuits. FMCAD 2016: 41-48