Programs as polygraphs: computability and complexity

Abstract – This study presents Albert Burroni’s polygraphs as an algebraic and graphical description of first-order functional programs, where functions can have many outputs. We prove that polygraphic programs form a Turing-complete computational model. Using already-known termination orders for polygraphs, we define simple programs as a special class of polygraphs equipped with a notion of polynomial interpretation. We prove that computations in a simple program have a polynomial size and conclude that simple programs compute exactly polynomial-time functions. Keywords – Polygraph, program, computabil

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Guillaume Bonfante, Yves Guiraud
• Keywords: CORR 2007, Education, Polygraph, Simple Programs, first-order Functional Programs