Applicative theories for logarithmic complexity classes

We present applicative theories of words corresponding to weak, and especially logarithmic, complexity classes. The theories for the logarithmic hierarchy and alternating logarithmic time formalise function algebras with concatenation recursion as main principle. We present two theories for logarithmic space where the first formalises a new two-sorted algebra which is very similar to Cook and Bellantoni's famous two-sorted algebra B for polynomial time [4]. The second theory describes logarithmic space by formalising concatenation- and sharply bounded recursion. All theories contain the predicates WW representing words, and VV representing temporary inaccessible words. They are inspired by Cantini's theories [6] formalising B.

Exact Unification and Admissibility

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed. In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type. These results are obtained via an algebraic interpretation of exact unification, inspired by Ghilardi's algebraic approach to equational unification.

Artificial Neural Nets with Interaction of Afferents

The aim is to obtain computationally more powerful, neuro physiologically founded, artificial neurons and neural nets. Artificial Neural Nets (ANN) of the Perceptron type evolved from the original proposal by McCulloch an Pitts classical paper [1]. Essentially, they keep the computing structure of a linear machine followed by a non linear operation. The McCulloch-Pitts formal neuron (which was never considered by the author’s to be models of real neurons) consists of the simplest case of a linear computation of the inputs followed by a threshold. Networks of one layer cannot compute anylogical function of the inputs, but only those which are linearly separable. Thus, the simple exclusive OR (contrast detector) function of two inputs requires two layers of formal neurons

On abstraction-carrying code and certificate-size reduction

Abstraction-Carrying Code (ACC) is a framework for mobile code safety in which the code supplier provides a program together with an abstraction (or abstract model of the program) whose validity entails compliance with a predefined safety policy. The abstraction plays thus the role of safety certificate and its generation is carried out automatically by a fixed-point analyzer. The advantage of providing a (fixed-point) abstraction to the code consumer is that its validity is checked in a single pass (i.e., one iteration) of an abstract interpretation-based checker. A main challenge to make ACC useful in practice is to reduce the size of certificates as much as possible, while at the same time not increasing checking time. Intuitively, we only include in the certificate the information which the checker is unable to reproduce without iterating. We introduce the notion of reduced certifícate which characterizes the subset of the abstraction which a checker needs in order to validate (and re-construct) the full certificate in a single pass. Based on this notion, we show how to instrument a generic analysis algorithm with the necessary extensions in order to identify the information relevant to the checker.

User-definable resource usage bounds analysis for java bytecode

Automatic cost analysis of programs has been traditionally concentrated on a reduced number of resources such as execution steps, time, or memory. However, the increasing relevance of analysis applications such as static debugging and/or certiflcation of user-level properties (including for mobile code) makes it interesting to develop analyses for resource notions that are actually application-dependent. This may include, for example, bytes sent or received by an application, number of files left open, number of SMSs sent or received, number of accesses to a datábase, money spent, energy consumption, etc. We present a fully automated analysis for inferring upper bounds on the usage that a Java bytecode program makes of a set of application programmer-deflnable resources. In our context, a resource is defined by programmer-provided annotations which state the basic consumption that certain program elements make of that resource. From these deflnitions our analysis derives functions which return an upper bound on the usage that the whole program (and individual blocks) make of that resource for any given set of input data sizes. The analysis proposed is independent of the particular resource. We also present some experimental results from a prototype implementation of the approach covering a signiflcant set of interesting resources.

Some issues in analysis and specialization of modular ciao-prolog programs

Separating programs into modules is a well-known technique which has proven very useful in program development and maintenance. Starting by introducing a number of possible scenarios, in this paper we study different issues which appear when developing analysis and specialization techniques for modular logic programming. We discuss a number of design alternatives and their consequences for the different scenarios considered and describe where applicable the decisions made in the Ciao system analyzer and specializer. In our discussion we use the module system of Ciao Prolog. This is both for concreteness and because Ciao Prolog is a second-generation Prolog system which has been designed with global analysis and specialization in mind, and which has a strict module system. The aim of this work is not to provide a theoretical basis on modular analysis and specialization, but rather to discuss some interesting practical issues.

The ciao module system: A new module system for prolog

Ciao Prolog incorporates a module system which allows sepárate compilation and sensible creation of standalone executables. We describe some of the main aspects of the Ciao modular compiler, ciaoc, which takes advantage of the characteristics of the Ciao Prolog module system to automatically perform sepárate and incremental compilation and efficiently build small, standalone executables with competitive run-time performance, ciaoc can also detect statically a larger number of programming errors. We also present a generic code processing library for handling modular programs, which provides an important part of the functionality of ciaoc. This library allows the development of program analysis and transformation tools in a way that is to some extent orthogonal to the details of module system design, and has been used in the implementation of ciaoc and other Ciao system tools. We also describe the different types of executables which can be generated by the Ciao compiler, which offer different tradeoffs between executable size, startup time, and portability, depending, among other factors, on the linking regime used (static, dynamic, lazy, etc.). Finally, we provide experimental data which illustrate these tradeoffs.

The ciao modular, standalone compiler and its generic program processing library

Ciao Prolog incorporates a module system which allows sepárate compilation and sensible creation of standalone executables. We describe some of the main aspects of the Ciao modular compiler, ciaoc, which takes advantage of the characteristics of the Ciao Prolog module system to automatically perform sepárate and incremental compilation and efficiently build small, standalone executables with competitive run-time performance, ciaoc can also detect statically a larger number of programming errors. We also present a generic code processing library for handling modular programs, which provides an important part of the functionality of ciaoc. This library allows the development of program analysis and transformation tools in a way that is to some extent orthogonal to the details of module system design, and has been used in the implementation of ciaoc and other Ciao system tools. We also describe the different types of executables which can be generated by the Ciao compiler, which offer different tradeoffs between executable size, startup time, and portability, depending, among other factors, on the linking regime used (static, dynamic, lazy, etc.). Finally, we provide experimental data which illustrate these tradeoffs.

A system for automatically generating documentation for (C)LP programs

We describe lpdoc, a tool which generates documentation manuals automatically from one or more logic program source files, written in ISO-Prolog, Ciao, and other (C)LP languages. It is particularly useful for documenting library modules, for which it automatically generates a rich description of the module interface. However, it can also be used quite successfully to document full applications. A fundamental advantage of using lpdoc is that it helps maintaining a true correspondence between the program and its documentation, and also identifying precisely to what version of the program a given printed manual corresponds. The quality of the documentation generated can be greatly enhanced by including within the program text assertions (declarations with types, modes, etc.) for the predicates in the program, and machine-readable comments. One of the main novelties of lpdoc is that these assertions and comments are written using the Ciao system assertion language, which is also the language of communication between the compiler and the user and between the components of the compiler. This allows a significant synergy among specification, documentation, optimization, etc. A simple compatibility library allows conventional (C)LP systems to ignore these assertions and comments and treat normally programs documented in this way. The documentation can be generated in many formats including texinfo, dvi, ps, pdf, info, html/css, Unix nroff/man, Windows help, etc., and can include bibliographic citations and images. lpdoc can also generate “man” pages (Unix man page format), nicely formatted plain ascii “readme” files, installation scripts useful when the manuals are included in software distributions, brief descriptions in html/css or info formats suitable for inclusion in on-line indices of manuals, and even complete WWW and info sites containing on-line catalogs of documents and software distributions. The lpdoc manual, all other Ciao system manuals, and parts of this paper are generated by lpdoc.

A card Game Description Language

We present initial research regarding a system capable of generating novel card games. We furthermore propose a method for com- putationally analysing existing games of the same genre. Ultimately, we present a formalisation of card game rules, and a context-free grammar G cardgame capable of expressing the rules of a large variety of card games. Example derivations are given for the poker variant Texashold?em , Blackjack and UNO. Stochastic simulations are used both to verify the implementation of these well-known games, and to evaluate the results of new game rules derived from the grammar. In future work, this grammar will be used to evolve completely novel card games using a grammar- guided genetic program.

Reachability-based acyclicity analysis by Abstract Interpretation

In programming languages with dynamic use of memory, such as Java, knowing that a reference variable x points to an acyclic data structure is valuable for the analysis of termination and resource usage (e.g., execution time or memory consumption). For instance, this information guarantees that the depth of the data structure to which x points is greater than the depth of the data structure pointed to by x.f for any field f of x. This, in turn, allows bounding the number of iterations of a loop which traverses the structure by its depth, which is essential in order to prove the termination or infer the resource usage of the loop. The present paper provides an Abstract-Interpretation-based formalization of a static analysis for inferring acyclicity, which works on the reduced product of two abstract domains: reachability, which models the property that the location pointed to by a variable w can be reached by dereferencing another variable v (in this case, v is said to reach w); and cyclicity, modeling the property that v can point to a cyclic data structure. The analysis is proven to be sound and optimal with respect to the chosen abstraction.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

Mathematica Balkanica New Series Book Volume 24 2010

Muharem Avdispahic 1 Coordinator of the TEMPUS Project SEE Doctoral Studies in Mathematical Sciences (144703-TEMPUS-2008-BA-TEMPUS-JPCR) The main goals of the TEMPUS Project ”SEE Doctoral Studies in Math- ematical Sciences”, funded by European Commission under the TEMPUS IV first call, consist of the development of a model of structured doctoral studies in Mathematical Sciences involving the network of Western Balkans universi- ties, the curricula design based on the existing strenghts and tendencies in the areas of Pure Mathematics, Applied Mathematics and Theoretical Computer Science and the first phase of implementation of the agreed model during the SEE Doctoral Year in Mathematical Sciences 2011. A decisive step in this direction was ”SEE Young Researchers Workshop” held in Ohrid, FYR Macedonia, September 16-20, 2009, as a part of the Math- ematical Society of South-Eastern Europe (MASSEE) International Congress on Mathematics - MICOM 2009. MICOM 2009 continued the tradition of two previous highly successful MASSEE congresses that took place in Bulgaria in 2003 and in Cyprus in 2006. This volume of the journal Mathematika Balkanica contains the talks de- livered at Ohrid Workshop by South-Eastern European PhD students in various stage of their research towards a doctoral degree in mathematics or informat- ics. Facilitating publication efforts of young researchers from the universities of Sarajevo, Tuzla, Belgrade, Skopje, Stip, Graz, and Sofia fully coincides with MASSEE goals to promote, organize and support scientific, research and edu- cational activities in South-Eastern Europe. The consent of the Editorial Board of Mathematica Balkanica to publish ”SEE Young Researchers Workshop” contributions aptly meets intentions of European reform processes aimed at creating the European Higher Education Area and European Research Area. It is an encouragement to these young researchers in the first place and at the same time an encouragement to their institutions in overcoming fragmentation and enhancing their capacities through fostering reciprocal development of human resources.