Related papers: Automated Amortised Analysis of Skew Heaps and Lef…
We introduce a novel amortised resource analysis couched in a type-and-effect system. Our analysis is formulated in terms of the physicist's method of amortised analysis, and is potential-based. The type system makes use of logarithmic…
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-)…
Leftist heaps and skew heaps are two well-known data structures for mergeable priority queues. Leftist heaps are constructed for efficiency in the worst-case sense whereas skew heaps are self-adjusting, designed for efficiency in the…
We introduce a novel amortised resource analysis based on a potential-based type system. This type system gives rise to logarithmic and polynomial bounds on the runtime complexity and is the first such system to exhibit logarithmic…
Amortized analysis is a cost analysis technique for data structures in which cost is studied in aggregate: rather than considering the maximum cost of a single operation, one bounds the total cost encountered throughout a session.…
We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within…
The integration of large language models (LLMs) with external tools has significantly expanded the capabilities of AI agents. However, as the diversity of both LLMs and tools increases, selecting the optimal model-tool combination becomes a…
We propose an amortized analysis that approximates the resource usage of a Haskell expression. Using the plugin API of GHC, we convert the Haskell code into a simplified representation called GHC Core. We then apply a type-based system…
The combination of LLM agents with external tools enables models to solve complex tasks beyond their knowledge base. Human-designed tools are inflexible and restricted to solutions within the scope of pre-existing tools created by experts.…
We introduce a novel resource analysis for typed term rewrite systems based on a potential-based type system. This type system gives rise to polynomial bounds on the innermost runtime complexity. We relate the thus obtained amortised…
In this paper we establish an automated amortised resource analysis for term rewrite systems. The method is presented in an annotated type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed term…
This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs. The analysis is naturally compositional, parametric in the cost model, and supports higher order functions and…
We consider enhancing large language models (LLMs) for complex planning tasks. While existing methods allow LLMs to explore intermediate steps to make plans, they either depend on unreliable self-verification or external verifiers to…
Despite the popularity of Shapley Values in explaining neural text classification models, computing them is prohibitive for large pretrained models due to a large number of model evaluations. In practice, Shapley Values are often estimated…
Automated analysis for engineering structures offers considerable potential for boosting efficiency by minimizing repetitive tasks. Although AI-driven methods are increasingly common, no systematic framework yet leverages Large Language…
Multilevel models (MLMs) are a central building block of the Bayesian workflow. They enable joint, interpretable modeling of data across hierarchical levels and provide a fully probabilistic quantification of uncertainty. Despite their…
An automated resource analysis technique is introduced, targeting a Call-By-Push-Value abstract machine, with memory prediction as a practical goal. The machine has a polymorphic and linear type system enhanced with a first-order logical…
We develop a weakest-precondition-style calculus \`a la Dijkstra for reasoning about amortized expected runtimes of randomized algorithms with access to dynamic memory - the $\textsf{aert}$ calculus. Our calculus is truly quantitative, i.e.…
Since the seminal work by Angluin and the introduction of the L*-algorithm, active learning of automata by membership and equivalence queries has been extensively studied to learn various extensions of automata. For weighted automata,…
The smooth heap is a recently introduced self-adjusting heap [Kozma, Saranurak, 2018] similar to the pairing heap [Fredman, Sedgewick, Sleator, Tarjan, 1986]. The smooth heap was obtained as a heap-counterpart of Greedy BST, a binary search…