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Exhausters are families of compact, convex sets which provide minmax or maxmin representations of positively homogeneous functions and they are efficient tools for the study of nonsmooth function. Upper and lower exhausters of positively…
Any two-way finite state automaton is equivalent to some one-way finite state automaton. This well-known result, shown by Rabin and Scott and independently by Shepherdson, states that two-way finite state automata (even non-deterministic)…
The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful…
This paper describes an algorithm for the compilation of a two (or more) level orthographic or phonological rule notation into finite state transducers. The notation is an alternative to the standard one deriving from Koskenniemi's work: it…
We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
We introduce novel dynamic oracles for training two of the most accurate known shift-reduce algorithms for constituent parsing: the top-down and in-order transition-based parsers. In both cases, the dynamic oracles manage to notably…
The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
Using maximum instead of sum, nonlinear Baskakov operator of maximum product kind is introduced by Bede et al. The present paper deals with the approximation processes for this operator. Especially in , it was indicated that the order of…
We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language…
Occurrences of a factor $w$ in an infinite uniformly recurrent sequence ${\bf u}$ can be encoded by an infinite sequence over a finite alphabet. This sequence is usually denoted ${\bf d_{\bf u}}(w)$ and called the derived sequence to $w$ in…
Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2)…
This thesis presents a broad-coverage probabilistic top-down parser, and its application to the problem of language modeling for speech recognition. The parser builds fully connected derivations incrementally, in a single pass from…
The Suffix Array $SA_S[1\ldots n]$ of an $n$-length string $S$ is a lexicographically sorted array of the suffixes of $S$. The suffix array is one of the most well known and widely used data structures in string algorithms. We present a…
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
Simultaneous translation, which translates sentences before they are finished, is useful in many scenarios but is notoriously difficult due to word-order differences. While the conventional seq-to-seq framework is only suitable for…
In a previous paper, the sup-interpretation method was proposed as a new tool to control memory resources of first order functional programs with pattern matching by static analysis. Basically, a sup-interpretation provides an upper bound…
Constructing accurate and automatic solvers of math word problems has proven to be quite challenging. Prior attempts using machine learning have been trained on corpora specific to math word problems to produce arithmetic expressions in…