AND and/or OR: Uniform Polynomial-Size Circuits

We investigate the complexity of uniform OR circuits and AND circuits of polynomial-size and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant (0/1) gates. As is the norm for Boolean circuits, our circuits have multiple sink gates, which implies that an OR circuit computes an OR function on some subset of its input variables. Determining that subset amounts to solving a number of reachability questions on a polynomial-size directed graph (which input gates are connected to the output gate?), taken from a very sparse set of graphs. However, it is not obvious whether or not this (restricted) reachability problem can be solved, by say, uniform AC^0 circuits (constant depth, polynomial-size, AND, OR, NOT gates). This is one reason why characterizing the power of these simple-looking circuits in terms of uniform classes turns out to be intriguing. Another is that the model itself seems particularly natural and worthy of study. Our goal is the systematic characterization of uniform polynomial-size OR circuits, and AND circuits, in terms of known uniform machine-based complexity classes. In particular, we consider the languages reducible to such uniform families of OR circuits, and AND circuits, under a variety of reduction types. We give upper and lower bounds on the computational power of these language classes. We find that these complexity classes are closely related to tallyNL, the set of unary languages within NL, and to sets reducible to tallyNL. Specifically, for a variety of types of reductions (many-one, conjunctive truth table, disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL classes. Then, some of these OR classes are shown to coincide, and some are proven to be distinct. We give analogous results for AND circuits. Finally, for many of our OR circuit classes, and analogous AND circuit classes, we prove whether or not the two classes coincide, although we leave one such inclusion open.Comment: In Proceedings MCU 2013, arXiv:1309.104

HUDDL for description and archive of hydrographic binary data

Many of the attempts to introduce a universal hydrographic binary data format have failed or have been only partially successful. In essence, this is because such formats either have to simplify the data to such an extent that they only support the lowest common subset of all the formats covered, or they attempt to be a superset of all formats and quickly become cumbersome. Neither choice works well in practice. This paper presents a different approach: a standardized description of (past, present, and future) data formats using the Hydrographic Universal Data Description Language (HUDDL), a descriptive language implemented using the Extensible Markup Language (XML). That is, XML is used to provide a structural and physical description of a data format, rather than the content of a particular file. Done correctly, this opens the possibility of automatically generating both multi-language data parsers and documentation for format specification based on their HUDDL descriptions, as well as providing easy version control of them. This solution also provides a powerful approach for archiving a structural description of data along with the data, so that binary data will be easy to access in the future. Intending to provide a relatively low-effort solution to index the wide range of existing formats, we suggest the creation of a catalogue of format descriptions, each of them capturing the logical and physical specifications for a given data format (with its subsequent upgrades). A C/C++ parser code generator is used as an example prototype of one of the possible advantages of the adoption of such a hydrographic data format catalogue

A Formal Framework for Linguistic Annotation

`Linguistic annotation' covers any descriptive or analytic notations applied to raw language data. The basic data may be in the form of time functions -- audio, video and/or physiological recordings -- or it may be textual. The added notations may include transcriptions of all sorts (from phonetic features to discourse structures), part-of-speech and sense tagging, syntactic analysis, `named entity' identification, co-reference annotation, and so on. While there are several ongoing efforts to provide formats and tools for such annotations and to publish annotated linguistic databases, the lack of widely accepted standards is becoming a critical problem. Proposed standards, to the extent they exist, have focussed on file formats. This paper focuses instead on the logical structure of linguistic annotations. We survey a wide variety of existing annotation formats and demonstrate a common conceptual core, the annotation graph. This provides a formal framework for constructing, maintaining and searching linguistic annotations, while remaining consistent with many alternative data structures and file formats.Comment: 49 page

An implementation and analysis of the Abstract Syntax Notation One and the basic encoding rules

The details of abstract syntax notation one standard (ASN.1) and the basic encoding rules standard (BER) that collectively solve the problem of data transfer across incompatible host environments are presented, and a compiler that was built to automate their use is described. Experiences with this compiler are also discussed which provide a quantitative analysis of the performance costs associated with the application of these standards. An evaluation is offered as to how well suited ASN.1 and BER are in solving the common data representation problem

kLog: A Language for Logical and Relational Learning with Kernels

We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials