Related papers: Random Context and Semi-Conditional Insertion-Dele…
In this article, we consider for the first time the operations of insertion and deletion working in a matrix controlled manner. We show that, similarly as in the case of context-free productions, the computational power is strictly…
In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph:…
Recent investigations show insertion-deletion systems of small size that are not complete and cannot generate all recursively enumerable languages. However, if additional computational distribution mechanisms like P systems are added, then…
We consider the (one-dimensional) array counterpart of contextual as well as insertion and deletion string grammars and consider the operations of array insertion and deletion in array grammars. First we show that the emptiness problem for…
We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the…
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet…
This paper solves an open problem concerning the generative power of nonerasing context-free rewriting systems using a simple mechanism for checking for context dependencies, in the literature known as semi-conditional grammars of degree…
Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
A recent study on structural properties of regular and context-free languages has greatly promoted our basic understandings of the complex behaviors of those languages. We continue the study to examine how regular languages behave when they…
In this paper, we study the surprising impact that truncating text embeddings has on downstream performance. We consistently observe across 6 state-of-the-art text encoders and 26 downstream tasks, that randomly removing up to 50% of…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
This work continues the study of linear error correcting codes against adversarial insertion deletion errors (insdel errors). Previously, the work of Cheng, Guruswami, Haeupler, and Li \cite{CGHL21} showed the existence of asymptotically…
In this paper we consider the two major computational effects of states and exceptions, from the point of view of diagrammatic logics. We get a surprising result: there exists a symmetry between these two effects, based on the well-known…
Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an…
An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (meta-states) and inference algorithms are run…
Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in…
A noncontextual system of random variables may become contextual if one adds to it a set of new variables, even if each of them is obtained by the same context-wise function of the old variables. This fact follows from the definition of…
We study codes that are list-decodable under insertions and deletions. Specifically, we consider the setting where a codeword over some finite alphabet of size $q$ may suffer from $\delta$ fraction of adversarial deletions and $\gamma$…
We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice.…