Automated Expected Amortised Cost Analysis of Probabilistic Data Structures

Abstract

In this paper, we present the first fully-automated expected amortised cost analysis of self-adjusting data structures, that is, of randomised splay trees, randomised splay heaps and randomised meldable heaps, which so far have only (semi-)manually been analysed in the literature. Our analysis is stated as a type-and-effect system for a first-order functional programming language with support for sampling over discrete distributions, non-deterministic choice and a ticking operator. The latter allows for the specification of fine-grained cost models. We state two soundness theorems based on two different—but strongly related—typing rules of ticking, which account differently for the cost of non-terminating computations. Finally we provide a prototype implementation able to fully automatically analyse the aforementioned case studies."Image missing"

Proving Almost-Sure Innermost Termination of Probabilistic Term Rewriting Using Dependency Pairs

“…While there exist many automatic approaches to prove (P)AST of imperative programs on numbers (e.g., [1,4,11,15,21,[24][25][26][32][33][34]36]), there are only few automatic approaches for programs with complex non-tail recursive structure [7,12], and even less approaches which are also suitable for algorithms on recursive data structures [3,6,31,39]. The approach of [39] focuses on algorithms on lists and [31] mainly targets algorithms on trees, but they cannot easily be adjusted to other (possibly user-defined) data structures. The calculus of [6] considers imperative programs with stack, heap, and pointers, but it is not yet automated.…”

“…The calculus of [6] considers imperative programs with stack, heap, and pointers, but it is not yet automated. Moreover, the approaches of [3,6,31,39] analyze expected runtime, while we focus on AST.…”