From Boolean Functional Equations to Control Software

TL;DR

This paper introduces an algorithm that converts boolean relations into efficient C code implementations with controlled size and execution time, addressing a gap in software synthesis methods compared to hardware synthesis.

Contribution

It presents a novel algorithm that generates C code from OBDD representations of boolean relations, optimizing for size and worst-case execution time in software synthesis.

Findings

Generates C code with size comparable to OBDD for F

Achieves worst-case execution time at most O(nr)

Addresses a gap in software synthesis methods

Abstract

Many software as well digital hardware automatic synthesis methods define the set of implementations meeting the given system specifications with a boolean relation K. In such a context a fundamental step in the software (hardware) synthesis process is finding effective solutions to the functional equation defined by K. This entails finding a (set of) boolean function(s) F (typically represented using OBDDs, Ordered Binary Decision Diagrams) such that: 1) for all x for which K is satisfiable, K(x, F(x)) = 1 holds; 2) the implementation of F is efficient with respect to given implementation parameters such as code size or execution time. While this problem has been widely studied in digital hardware synthesis, little has been done in a software synthesis context. Unfortunately the approaches developed for hardware synthesis cannot be directly used in a software context. This motivates investigation of effective methods to solve the above problem when F has to be implemented with software. In this paper we present an algorithm that, from an OBDD representation for K, generates a C code implementation for F that has the same size as the OBDD for F and a WCET (Worst Case Execution Time) at most O(nr), being n = |x| the number of arguments of functions in F and r the number of functions in F.