AVANZINI , Martin

Term rewriting has been used as a formal model to reason about the complexity of logic, functional , and imperative programs. In contrast to term rewriting, term graph rewriting permits sharing of common sub-expressions, and consequently is able to capture more closely reasonable implementations of rule based languages. However, the automated...

This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three ingredients: a powerful type system for size analysis and a sound type inference procedure for it, a ticking monadic transformation, and constraint solving. Noticeably, the presented methodology can be fully...

We study how the adoption of an evaluation mechanism with sharing and memoization impacts the class of functions which can be computed in polynomial time. We first show how a natural cost model in which lookup for an already computed value has no cost is indeed invariant. As a corollary, we then prove that the most general notion of ramified...

We study how the adoption of an evaluation mechanism with sharing and memoization impacts the class of functions which can be computed in polynomial time. We first show how a natural cost model in which lookup for an already computed result has no cost is indeed invariant. As a corollary, we then prove that the most general notion of ramified...

Nowadays certification is widely employed by automated termination tools for term rewriting, where certifiers support most available techniques. In complexity analysis, the situation is quite different. Although tools support certification in principle, current certifiers implement only the most basic technique, namely, suitably tamed versions...

In this paper we present TcT v3.0, the latest version of our fully automated complexity analyser.TcT implements our framework for automated complexity analysis and focuses on extensibility and automation. TcT is open with respect to the input problem under investigation and the resource metric in question.It is the most powerful tool in the...

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In this work, we study the fully automated inference of expected result values of probabilistic programs in the presence of natural programming constructs such as procedures, local variables and recursion. While crucial, capturing these constructs becomes highly non-trivial. The key contribution is the definition of a term representation,...

The efficacy of address space layout randomization has been formally demonstrated in a shared-memory model by Abadi et al., contingent on specific assumptions about victim programs. However, modern operating systems, implementing layout randomization in the kernel, diverge from these assumptions and operate on a separate memory model with...

We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of first-order term rewrite systems. This is done while carefully analysing complexity preservation and...

We define a continuation-passing style (CPS) translation for a typed-calculus with probabilistic choice, unbounded recursion, and a tick operator-for modeling cost. The target language is a (non-probabilistic)-calculus, enriched with a type of extended positive reals and a fixpoint operator. We then show that applying the CPS transform of an...

We show that complexity analysis of probabilistic higher-order functional programs can be carried out compositionally by way of a type system. The introduced type system is a significant extension of linear dependent types. On the one hand, the presence of probabilistic effects requires adopting a form of dynamic distribution type, subject to a...

We show that complexity analysis of probabilistic higher-order functional programs can be carried out composi-tionally by way of a type system. The introduced type system is a significant extension of refinement types. On the one hand, the presence of probabilistic effects requires adopting a form of dynamic distribution type, subject to a...

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite systems are considered. Two instances of the interpretation method-polynomial and matrix...

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite systems are considered. Two instances of the interpretation method—polynomial and matrix...

We introduce a new kind of expectation transformer for a mixed classical-quantum programming language. Our semantic approach relies on a new notion of a cost structure, which we introduce and which can be seen as a specialisation of the Kegelspitzen of Keimel and Plotkin. We show that our weakest precondition analysis is both sound and adequate...