Verification Column

Abstract

Many verification problems can be formulated as a language inclusion problem where the task is to decide whether the language of the system model (given by the runs of the system) is contained in the language induced by a logical specification. The corresponding verification problem for non-functional properties is the quantitative inclusion problem where both the system model and the specification are given by weighted automata and the task is to decide whether the weight for each input string in the automaton for the system is less than that in the automaton for the specification. Here, the weight of a string is defined as an aggregate value of the weights assigned to the states and/or transitions in that string. So, the essential task of the quantitative inclusion problem is to compare the aggregate weight of two input strings. Comparator automata yield an elegant automata-based approach to reason about multiple instances of the quantitative inclusion problem and other algorithmic problems for weighted structures. Speaking roughly, they are defined as automata that take as input two infinite weighted sequences and relate their aggregate values. Among others, they have used to introduce generic algorithms for quantitative inclusion problems and other verification problems for weighted system models. The article by Sugumal Bansal presents an introduction to comparator automata and a summary of their application areas.