Regular Combinators for String Transformations

We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using two-way finite-state transducers, (one-way) cost register automata, and MSO-definable graph transformations. In this paper, we give an algebraic and machine-independent characterization of this class analogous to the definition of regular languages by regular expressions. When the monoid is commutative, we prove that every regular function can be constructed from constant functions using the combinators of choice, split sum, and iterated sum, that are analogs of union, concatenation, and Kleene-*, respectively, but enforce unique (or unambiguous) parsing. Our main result is for the general case of non-commutative monoids, which is of particular interest for capturing regular string-to-string transformations for document processing. We prove that the following additional combinators suffice for constructing all regular functions: (1) the left-additive versions of split sum and iterated sum, which allow transformations such as string reversal; (2) sum of functions, which allows transformations such as copying of strings; and (3) function composition, or alternatively, a new concept of chained sum, which allows output values from adjacent blocks to mix.Comment: This is the full version, with omitted proofs and constructions, of the conference paper currently in submissio

EF+EX Forest Algebras

We examine languages of unranked forests definable using the temporal operators EF and EX. We characterize the languages definable in this logic, and various fragments thereof, using the syntactic forest algebras introduced by Bojanczyk and Walukiewicz. Our algebraic characterizations yield efficient algorithms for deciding when a given language of forests is definable in this logic. The proofs are based on understanding the wreath product closures of a few small algebras, for which we introduce a general ideal theory for forest algebras. This combines ideas from the work of Bojanczyk and Walukiewicz for the analogous logics on binary trees and from early work of Stiffler on wreath product of finite semigroups

Which Classes of Origin Graphs Are Generated by Transducers.

We study various models of transducers equipped with origin information. We consider the semantics of these models as particular graphs, called origin graphs, and we characterise the families of such graphs recognised by streaming string transducers

Estimation and Evaluation of Some Interdependencies of Environmental Conditions, Welfare Standards, Health Services, and Health Status

The building of complex models of socio-economic development especially on the regional level, requires the knowledge of important relations and feedbacks between the health status of a population and the indices describing welfare standards such as environmental conditions, income level, and public services. In developing a family of submodels of national health care systems for use by health service planners, it is important to consider the environmental impact on health status as well, since the environment forms one of the most significant external subsystems influencing health care. Needless to say, more effort is needed in modeling the links between health care systems and the national economy. In this paper, a set of basic health standard relationships are postulated. Through this the consequences of resource allocation policies can be determined, thus aiding the decisionmaking process. Proposed formulae are estimated on Polish statistical data using cross-sectional analysis, and a critical evaluation of the significance of these relationships is given

A Concept of Modeling a Health Manpower Educational System

The paper presents some mathematical concepts of modeling a health manpower educational system. The importance of manpower resources, i.e., doctors, nurses, and other supporting staff, in the health services delivery process is widely recognized. Therefore, the research on resource supply models analyzing health manpower education was undertaken. First, the general structure of the health manpower educational system (HMES) was presented. Next the adapted methodology of modeling was described, followed by mare detailed presentations of: secondary medical school subsystems; medical academy subsystems; and postgraduate courses. Numerical examples from Poland of the application of proposed simulation techniques to medical academies were given. In addition, the forecasts of the number of medical doctors with Ph.D. degrees were presented. Then the utilization of resources in the education process was briefly described. The paper focused its attention on models for simulation purposes, but an optimization approach to the modeling of an educational system was also presented, proceeding naturally from simulation models

Undecidability of a weak version of MSO+U

We prove the undecidability of MSO on ω-words extended with the second-order predicate U1(X) which says that the distance between consecutive positions in a set X⊆N is unbounded. This is achieved by showing that adding U1 to MSO gives a logic with the same expressive power as MSO+U, a logic on ω-words with undecidable satisfiability. As a corollary, we prove that MSO on ω-words becomes undecidable if allowing to quantify over sets of positions that are ultimately periodic, i.e., sets X such that for some positive integer p, ultimately either both or none of positions x and x+p belong to X

Two-Way Visibly Pushdown Automata and Transducers

Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three following models are equivalent: deterministic two-way transducers, monadic second-order (MSO) transducers, and deterministic one-way automata equipped with a finite number of registers. Nested words are words with a nesting structure, allowing to model unranked trees as their depth-first-search linearisations. In this paper, we consider transformations from nested words to words, allowing in particular to produce unranked trees if output words have a nesting structure. The model of visibly pushdown transducers allows to describe such transformations, and we propose a simple deterministic extension of this model with two-way moves that has the following properties: i) it is a simple computational model, that naturally has a good evaluation complexity; ii) it is expressive: it subsumes nested word-to-word MSO transducers, and the exact expressiveness of MSO transducers is recovered using a simple syntactic restriction; iii) it has good algorithmic/closure properties: the model is closed under composition with a unambiguous one-way letter-to-letter transducer which gives closure under regular look-around, and has a decidable equivalence problem

The IIASA Health Care Allocation Model DRAM: Calibration Using Data from Poland

This paper presents a further application of DRAM, which was developed at IIASA to help health care planners in analyzing and evaluating resource allocation decisions. This time an effort has been made to calibrate DRAM for in-patient hospital care in Poland. The parameterization procedures have been performed for eight patient categories (child surgery, general medicine, general surgery, obstetrics and gynaecology, ophthalmology, otorhinolaryngology, traumatic and orthopaedic surgery, and paediatrics) and three resource types (hospital beds, hospital doctors, and hospital nurses). The data set consists of 22 administrative regions in 1969. The ability with which the submodels were able to reproduce the actual allocations varied from one treatment category to another. (Six submodels were used: 3 one-resource, 2 two-resource, and 1 three-resource submodels.) Thus following the critical analysis in section 4.11, the three patient categories (general medicine, general surgery, and obstetrics and gynaecology) that appeared to reproduce the allocation patterns most successfully were chosen. The reevaluated DRAM for reduced number of categories and for two resources -- hospital beds and hospital doctors -- was then used to predict resource allocations in some regions

Mean-payoff Automaton Expressions

Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic mean-payoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm