Related papers: Weighted GKAT: Completeness and Complexity
In this paper, we introduce Target-Aware Weighted Training (TAWT), a weighted training algorithm for cross-task learning based on minimizing a representation-based task distance between the source and target tasks. We show that TAWT is easy…
We present a Coq library about Kleene algebra with tests, including a proof of their completeness over the appropriate notion of languages, a decision procedure for their equational theory, and tools for exploiting hypotheses of a…
The Kleene theorem establishes a fundamental link between automata and expressions over the free monoid. Numerous generalisations of this result exist in the literature. Lifting this result to a weighted setting has been widely studied.…
Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a…
We develop StacKAT, a network verification language featuring loops, finite state variables, nondeterminism, and - most importantly - access to a stack with accompanying push and pop operations. By viewing the variables and stack as the…
This paper connects the classes of weighted alternating finite automata (WAFA), weighted finite tree automata (WFTA), and polynomial automata (PA). First, we investigate the use of trees in the run semantics for weighted alternating…
We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with control structures, such as conditionals and loops. POCKA enables reasoning about programs that can access…
In this work we investigate Weighted Model Enumeration (WME): given a Boolean formula and a weight function over its satisfying assignments, enumerate models while accounting for their weights. This setting supports weight-driven queries,…
Computer-aided translation (CAT), the use of software to assist a human translator in the translation process, has been proven to be useful in enhancing the productivity of human translators. Autocompletion, which suggests translation…
Masked Language Modeling (MLM) is widely used to pretrain language models. The standard random masking strategy in MLM causes the pre-trained language models (PLMs) to be biased toward high-frequency tokens. Representation learning of rare…
Automatic Sign Language Translation requires the integration of both computer vision and natural language processing to effectively bridge the communication gap between sign and spoken languages. However, the deficiency in large-scale…
Multiset automata are a class of automata for which the symbols can be read in any order and obtain the same result. We investigate weighted multiset automata and show how to construct them from weighted regular expressions. We present…
Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
Models of complicated systems can be represented in different ways - in scientific papers, they are represented using natural language text as well as equations. But to be of real use, they must also be implemented as software, thus making…
We introduce a version of probabilistic Kleene algebra with angelic nondeterminism and a corresponding class of automata. Our approach implements semantics via distributions over multisets in order to overcome theoretical barriers arising…
Nondeterministic weighted automata are finite automata with numerical weights on transitions. They define quantitative languages L that assign to each word w a real number L(w). The value of an infinite word w is computed as the maximal…
Large language models (LLMs) show impressive performance in solving complex language tasks. However, its large number of parameters presents significant challenges for the deployment. So, compressing LLMs to low bits can enable to deploy on…
We investigate the equational theory for Kleene algebra terms with variable complements and constant complements -- (language) complement where it applies only to variables or constants -- w.r.t. languages. While the equational theory…
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…