On High-Quality Synthesis

In the synthesis problem, we are given a specification psi over input and output signals, and we synthesize a system that realizes psi: with every sequence of input signals, the system associates a sequence of output signals so that the generated computation satisfies psi. The above classical formulation of the problem is Boolean. First, correctness is Boolean: a computation satisfies the specification psi or does not satisfy it. Then, other important and interesting measures like the size of the synthesized system, its robustness, price, and so on, are ignored. The paper surveys recent efforts to address and formalize different aspects of quality of synthesized systems. We start with multi-valued specification formalisms, which refine the notion of correctness and enable the designer to specify quality, and continue to the quality measure of sensing: the detail in which the inputs should be read in order to generate a correct computation. The first part is based on the articles [1-3]. The second part is based on [4,5].