Related papers: On Decidability of 2-process Affine Models
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
We consider the problem of determining, given x, y in Z^k and a finite set F of affine functions on Z^k, whether y is reachable from x by applying the functions F. We also consider the analogous problem over N^k. These problems are known to…
A natural way to measure the power of a distributed-computing model is to characterize the set of tasks that can be solved in it. %the model. In general, however, the question of whether a given task can be solved in a given model is…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of…
By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…
Modeling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the…
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…
When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…
With the availability of large databases and recent improvements in deep learning methodology, the performance of AI systems is reaching or even exceeding the human level on an increasing number of complex tasks. Impressive examples of this…
We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task $T$ and a model $M$, we provide topological conditions for $T$ to be solvable in $M$. When applied to…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Higher-order processes with parameterization are capable of abstraction and application (migrated from the lambda-calculus), and thus are computationally more expressive. For the minimal higher-order concurrency, it is well-known that the…
The class of Basic Feasible Functionals BFF is the second-order counterpart of the class of first-order functions computable in polynomial time. We present several implicit characterizations of BFF based on a typed programming language of…
In this paper, we study the performance of affine policies for two-stage adjustable robust optimization problem with fixed recourse and uncertain right hand side belonging to a budgeted uncertainty set. This is an important class of…