Programs as polygraphs: computability and complexity
نویسندگان
چکیده
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.
منابع مشابه
Intensional properties of polygraphs
We present polygraphic programs, a subclass of Albert Burroni’s polygraphs, as a computational model, showing how these objects can be seen as first-order functional programs. We prove that the model is Turing complete. We use polygraphic interpretations, a termination proof method introduced by the second author, to characterize polygraphic programs that compute in polynomial time. We conclude...
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