Related papers: Liquid Amortization: Proving Amortized Complexity …
In this paper we initiate the study of the computational complexity of learning linear temporal logic (LTL) formulas from examples. We construct approximation algorithms for fragments of LTL and prove hardness results; in particular we…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this…
In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
We show that streams and lazy data structures are a natural idiom for programming with infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes, jump processes, Dirichlet processes, and Beta processes. The crucial…
Learned indexes leverage machine learning models to accelerate query answering in databases, showing impressive practical performance. However, theoretical understanding of these methods remains incomplete. Existing research suggests that…
We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…
We study the fully automated amortised analysis of purely functional data structures like skew heaps, as well as weight- and rank-biased leftist heaps. For that we generalise earlier works on automated amortised resource analysis by…
Kernel methods are widely used in machine learning and statistics for their flexibility and expressive power, yet their black-box nature limits adoption in high-stakes applications. Shapley value-based attribution methods such as SHAP, and…
A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…
Type-based amortised resource analysis following Hofmann and Jost---where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline---have been successful in…
Linearisability has become the standard correctness criterion for concurrent data structures, ensuring that every history of invocations and responses of concurrent operations has a matching sequential history. Existing proofs of…
Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics,…
The pairing heap is a simple "self-adjusting" implementation of a heap (priority queue). Inserting an item into a pairing heap or decreasing the key of an item takes O(1) time worst-case, as does melding two heaps. But deleting an item of…
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.…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
With the recent success of pre-trained models in NLP, a significant focus was put on interpreting their representations. One of the most prominent approaches is structural probing (Hewitt and Manning, 2019), where a linear projection of…
Hybrid complex analytics workloads typically include (i) data management tasks (joins, selections, etc. ), easily expressed using relational algebra (RA)-based languages, and (ii) complex analytics tasks (regressions, matrix decompositions,…