ACM Computing Surveys (CSUR)
On the computational complexity of imperative programming languages
Theoretical Computer Science - Implicit computational complexity
Certifying Polynomial Time and Linear/Polynomial Space for Imperative Programs
SIAM Journal on Computing
A flow calculus of mwp-bounds for complexity analysis
ACM Transactions on Computational Logic (TOCL)
The flow of data and the complexity of algorithms
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Static complexity analysis of higher order programs
FOPARA'09 Proceedings of the First international conference on Foundational and practical aspects of resource analysis
Closed-Form Upper Bounds in Static Cost Analysis
Journal of Automated Reasoning
Cost analysis of object-oriented bytecode programs
Theoretical Computer Science
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We present a new method for inferring complexity properties for imperative programs with bounded loops. The properties handled are: polynomial (or linear) boundedness of computed values, as a function of the input; and similarly for the running time.It is well known that complexity properties are undecidable for a Turing-complete programming language. Much work in program analysis overcomes this obstacle by relaxing the correctness notion: one does not ask for an algorithm that correctly decides whether the property of interest holds or not, but only for "yes" answers to be sound. In contrast, we reshaped the problem by defining a "core" programming language that is Turing-incomplete, but strong enough to model real programs of interest. For this language, our method is the first to give a certain answer; in other words, our inference is both sound and complete.The essence of the method is that every command is assigned a "complexity certificate", which is a concise specification of dependencies of output values on input. These certificates are produced by inference rules that are compositional and efficiently computable. The approach is inspired by previous work by Niggl and Wunderlich and by Jones and Kristiansen, but use a novel, more expressive kind of certificates.