Measuring the Gap: Algorithmic Approximation Bounds for the Space Complexity of Stream Specifications

15 pages•Published: March 26, 2017

Abstract

In previous work we presented an algorithmic procedure for analysing the space complexity of monitor specifications written in a fragment of predicate logic. These monitor specifications were developed for runtime monitoring of event streams. Our procedure provides accurate results for a large fragment of the possible specifications, but overestimates the space complexity of precisely those specifications which are more likely to be found in real world applications. Experiments hinted at a relationship between the extent our procedure over-approximates the space requirements of a specification and the quantifier structure of the specification. In this paper we provide a formalization of this relationship as approximation ratios, and are able to pinpoint ``good'' constructions, that is specifications using less memory. These results are first steps towards categorizing specifications based on memory efficiency.

Keyphrases: approximation, predicate logic, runtime verification, space complexity, stream monitoring

In: Mohamed Mosbah and Michael Rusinowitch (editors). SCSS 2017. The 8th International Symposium on Symbolic Computation in Software Science 2017, vol 45, pages 1-15.

Links:	https://easychair.org/publications/paper/Cvp
	https://doi.org/10.29007/t3jg