Regular Cost Functions, Part I: Logic and Algebra over Words

Regular Cost Functions, Part I: Logic and Algebra over Words

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to each input the two values “inside” and “outside”. This theory is a continuation of the works on distance automata and similar models. These models of automata h...

Safra-like constructions for regular cost functions over finite words

Regular cost functions have been introduced recently as an extension of the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. Cost functions are functions ranging over N∪{∞}, and considered modulo an equivalence which preserves the existence of bounds over each subset of the domain. A central result in the theory of r...

Linear temporal logic for regular cost functions

Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is that exact values are not considered, but only estimated. In this paper, we define an extension of Linear Temporal Logic (LTL) over finite words to describe...

Notes on P - Algebra ( 4 ) : Algebra over ProcessStructure , Part I .

We develop theory of algebra over processes, based on an abstract treatment of process structure. The abstract framework of process structures is developed (Part I), and, on its basis, theory of algebra is developed where the basic results including Birkho -like Variety Theorem are proved (Part II). We also discuss properties of signi cant concrete examples of algebras, taken from extant theori...

Regular Temporal Cost Functions