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Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
Rewriting is a formalism widely used in computer science and mathematical logic. When using rewriting as a programming or modeling paradigm, the rewrite rules describe the transformations one wants to operate and rewriting strategies are…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Essentially, in a reversible programming language, for each forward computation from state $S$ to state $S'$, there exists a constructive method to go backwards from state $S'$ to state $S$. Besides its theoretical interest, reversible…
Two objects are independent if they do not affect each other. Independence is well-understood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper…
Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…
A efficient incremental learning algorithm for classification tasks, called NetLines, well adapted for both binary and real-valued input patterns is presented. It generates small compact feedforward neural networks with one hidden layer of…
The ''trace reconstruction'' problem asks, given an unknown binary string $x$ and a channel that repeatedly returns ''traces'' of $x$ with each bit randomly deleted with some probability $p$, how many traces are needed to recover $x$? There…
It is well known that in a binary tree the external path length minus the internal path length is exactly 2n-2, where n is the number of external nodes. We show that a generalization of the formula holds for compacted tries, replacing the…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…
We introduce a coinductive definition of infinitary term rewriting. The setup is surprisingly simple, and has in contrast to the usual definitions of infinitary rewriting, neither need for ordinals nor for metric convergence. While the idea…
Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…
We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…
We consider all radiative corrections to the total electron-positron cross section showing how the renormalization group equation can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log etc.…
The standard algorithm to eliminate indirect left recursion takes a preventative approach, rewriting a grammar's rules so that indirect left recursion is no longer possible, rather than eliminating it only as and when it occurs. This…
This paper shows that a wide class of effective learning rules -- those that improve a scalar performance measure over a given time window -- can be rewritten as natural gradient descent with respect to a suitably defined loss function and…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…