Determining program complexity bounds is a fundamental problem with a variety of applications in software development. In this paper we present a novel approach for computing the asymptotic complexity bounds of non-deterministic recursive programs by solving dynamically inferred recurrence relations. Recurrences are inferred from program execution traces and solved using the annihilator method and Master Theorem to obtain closed-form solutions representing the complexity bounds.

Being able to detect program runtime complexity is useful in many tasks (e.g., checking expected performance and identifying potential security vulnerabilities). In this work, we introduce a new dynamic approach for inferring the asymptotic complexity bounds of recursive programs. From program execution traces, we learn recurrence relations and solve them using pattern matching to obtain closed-form solutions representing the complexity bounds of the program. This approach allows us to efficiently infer simple recurrence relations that represent nontrivial, potentially nonlinear polynomial and non-polynomial, complexity bounds. We present Dynaplex, a tool that implements these ideas to automatically generate recurrence relations from execution traces. Our preliminary results on popular and challenging recursive programs show that Dynaplex can learn precise relations capturing worst-case complexity bounds (e.g., O ( n log n ) for mergesort, O (2 n ) for Tower of Hanoi and O ( n 1.58 ) for Karatsuba’s multiplication algorithm).