Related papers: Adventures in time and space
A system of session types is introduced as induced by a Curry Howard correspondence applied to Bounded Linear Logic, and then extending the thus obtained type system with probabilistic choices and ground types. The obtained system satisfies…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
We describe a realizability framework for classical first-order logic in which realizers live in (a model of) typed {\lambda}{\mu}-calculus. This allows a direct interpretation of classical proofs, avoiding the usual negative translation to…
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
The goal of automatic resource bound analysis is to statically infer symbolic bounds on the resource consumption of the evaluation of a program. A longstanding challenge for automatic resource analysis is the inference of bounds that are…
We propose an automata-theoretic approach for reinforcement learning (RL) under complex spatio-temporal constraints with time windows. The problem is formulated using a Markov decision process under a bounded temporal logic constraint.…
Early experiments have suggested that program auralization can convey information about program structure [8]. Languages like Pascal contain classes of construct that are similar in nature allowing hierarchical classification of their…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In…
We propose a new order, the small polynomial path order (sPOP* for short). The order sPOP* provides a characterisation of the class of polynomial time computable function via term rewrite systems. Any polynomial time computable function…
For over a decade, researchers in formal methods tried to create formalisms that permit natural specification of systems and allow mathematical reasoning about their correctness. The availability of fully-automated reasoning tools enables…
Herman et al. pointed out that the insertion of run-time checks into a gradually typed program could hamper tail-call optimization and, as a result, worsen the space complexity of the program. To address the problem, they proposed a…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although…
Transactional memory (TM) allows concurrent processes to organize sequences of operations on shared \emph{data items} into atomic transactions. A transaction may commit, in which case it appears to have executed sequentially or it may…
Human reasoning is shaped by resource rationality -- optimizing performance under constraints. Recently, inference-time scaling has emerged as a powerful paradigm to improve the reasoning performance of Large Language Models by expanding…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
Humans and animals have the ability to reason and make predictions about different courses of action at many time scales. In reinforcement learning, option models (Sutton, Precup \& Singh, 1999; Precup, 2000) provide the framework for this…