Index sets for ω‐languages

An ω‐language is a set of infinite sequences (words) on a countable language, and corresponds to a set of real numbers in a natural way. Languages may be described by logical formulas in the arithmetical hierarchy and also may be described as the set of words accepted by some type of automata or Turing machine. Certain families of languages, such as the languages, may enumerated as P₀, P₁, … and then an index set associated to a given property R (such as finiteness) of languages is just the set of e such that P_e has the property. The complexity of index sets for 7 types of languages is determined for various properties related to the size of the language.     

Representing Utility Functions via Weighted Goals

We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, each characterized by a set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Machine dependent programming in common languages

It is suggested that we should distinguish between common programming languages and common solutions to specific problems. A solution may depend on specific machine characteristics even though it is expressed in a common language. It is further suggested that in future common programming languages this should be admitted openly by allowing the programmer to get access to the machine characteristics at hand through Environment Enquiries which are part of the language. Some specific examples of Environment Enquiries are given.An earlier version of this paper was published in ALGOL BULLETIN no. 18, October 1964.     

Regular Component Splittable Languages

Every infinite regular language contains a regular subset of the formuv+w for some words u, v, w, where v is not the empty word. The regularsubsets of the above form are called regular components. Some well-knowncontext-free languages, such as the Dyck language and the balanced language(over an alphabet X with |X| = 2), are decomposed as disjointunions of disjunctive languages. In this paper, we investigate thedecompositions of some of the regular languages and the context-freelanguages as disjoint unions of regular components. An infinite language iscalled regular component splittable if it can be expressed as a disjointunion of regular components and a finite set. We show that the Dycklanguage, the balanced language and some disjunctive context-free splittablelanguages are regular component splittable. We also present an example toshow that there is a disjunctive context-free language which is not regularcomponent splittable.     

A Language for Teaching Discrete-event Simulation

Courses which teach discrete-event simulation are based on many different simulation languages. The requirements for a language to support teaching simulation are discussed. In particular, it is recommended that such languages separate into distinct modules those aspects of simulation which are taught as separate topics. Implementation of the separation is discussed. The SEESIM language, developed as a teaching aid, is described, and examples of its use are given. Straightforward use of SEESIM can be learned quickly, yet the language provides facilities for a staged introduction to advanced concepts of simulation.     

Aspects of compact programs and directly executed languages

Some aspects of directly executed languages (DEL's) are described. Principles for the design of a DEL are given and in particular a survey of principles used to design a DEL yielding very compact programs. The idea of a refined display to get small address fields in DEL's for blockstructured languages is introduced. A comparison between IBM S/360 machine language and a specific DEL for the machine-oriented higher level language MARY gives quantitative results for the applicability of the techniques described.     

2 ω-finite automata and sets of obstructions of their languages

Nondeterministic finite Rabin-Scott’s automata without initial and final states (2ω-FA) are considered. In this paper, they are used to define so called sets of obstructions, used also in various algebraic systems, and to consider similar problems for the formal languages theory. Thus, we define sets of obstructions of languages (or, rather, 2ω-languages) of such automata. We obtain that each 2ω-language defined by 2 ω-FA has the set of obstruction being a regular language. And, vice versa, for each regular languageL (containing no proper subword of its another word), there exists a 2ω-FA havingL as the set of obstructions.     

New constructs for the description of combinatorial optimization problems in algebraic modeling languages

Algebraic languages are at the heart of many successful optimization modeling systems, yet they have been used with only limited success for combinatorial (or discrete) optimization. We show in this paper, through a series of examples, how an algebraic modeling language might be extended to help with a greater variety of combinatorial optimization problems. We consider specifically those problems that are readily expressed as the choice of a subset from a certain set of objects, rather than as the assignment of numerical values to variables. Since there is no practicable universal algorithm for problems of this kind, we explore a hybrid approach that employs a general-purpose subset enumeration scheme together with problem-specific directives to guide an efficient search.     

System function languages

In this paper we define the concept of a system function language which is a language generated by a system function. We identify system function languages with recursively enumerable sets which are non-simple and co-infinite. We then define restricted system function languages and identify them with recursive sets which are co-infinite. Finally we state and prove some independence and dependence relationships between system function languages and some of the more well-known decision problems. MSC: 03D05, 03D20, 03D25.     

Comparing eye movements during mathematical word problem solving in Chinese and German

Language plays an important role in word problem solving. Accordingly, the language in which a word problem is presented could affect its solution process. In particular, East-Asian, non-alphabetic languages are assumed to provide specific benefits for mathematics compared to Indo-European, alphabetic languages. By analyzing students’ eye movements in a cross-linguistic comparative study, we analyzed word problem solving processes in Chinese and German. 72 German and 67 Taiwanese undergraduate students solved PISA word problems in their own language. Results showed differences in eye movements of students, between the two languages. Moreover, independent cluster analyses revealed three clusters of reading patterns based on eye movements in both languages. Corresponding reading patterns emerged in both languages that were similarly and significantly associated with performance and motivational-affective variables. They explained more variance among students in these variables than between the languages alone. Our analyses show that eye movements of students during reading differ between the two languages, but very similar reading patterns exist in both languages. This result supports the assumption that the language alone is not a sufficient explanation for differences in students’ mathematical achievement, but that reading patterns are more strongly related to performance.     

Scenario formulation in an algebraic modelling language

Algebraic modelling languages have simplified management of many types of large linear programs but have not specifically supported stochastic modelling. This paper considers modelling language support for multistage stochastic linear recourse problems with finite distributions. We describe basic language requirements for formulation of finite event trees in algebraic modelling languages and show representative problems in AMPL using three commonly used scenario types.     

Two-dimensional homogeneous cubic systems: Classification and normal forms–III

This article is the third in a series of works devoted to two-dimensional homogeneous cubic systems. It considers the case where the homogeneous polynomial vector on the right-hand side of the system has a quadratic common factor with real zeros. The set of such systems is divided into classes of linear equivalence, in each of which a simplest system being a third-order normal form is distinguished on the basis of appropriately introduced structural and normalization principles. In fact, this normal form is determined by the coefficient matrix of the right-hand side, which is called a canonical form (CF). Each CF is characterized by an arrangement of nonzero elements, their specific normalization, and a canonical set of admissible values of the unnormalized elements, which ensures that the given CF belongs to a certain equivalence class. In addition, for each CF, (a) conditions on the coefficients of the initial system are obtained, (b) nonsingular linear substitutions reducing the right-hand side of a system satisfying these conditions to a given CF are specified, and (c) the values of the unnormalized elements of the CF thus obtained are given.     

Enhancing set constraint solvers with lexicographic bounds

Since their beginning in constraint programming, set solvers have been applied to a wide range of combinatorial search problems, such as bin-packing, set partitioning, circuit and combinatorial design. In this paper we present and evaluate a new means towards improving the practical reasoning power of Finite Set (FS) constraint solvers to better address such set problems with a particular attention to the challenging symmetrical set problems often cast as Combinatorial Design Problems (CDPs). While CDPs find a natural formulation in the language of sets, in constraint programming literature, alternative models are often used due to a lack of efficiency of traditional FS solvers. We first identify the main structural components of CDPs that render their modeling suitable to set languages but their solving a technical challenge. Our new prototype solver extends the traditional subset variable domain with lexicographic bounds that better approximate a set domain by satisfying the cardinality restrictions applied to the variable, and allow for active symmetry breaking using ordering constraints. Our contribution includes the formal and practical framework of the new solver implemented on top of a traditional set solver, and an empirical evaluation on benchmark CDPs.     

MAGIC: The Design and Use of an Interactive Modelling Language for Mathematical Programming

The desirability of computer aids for the building as well asthe solving of Mathematical Programming models is argued. Ashort survey is given of some of the distinct approaches possiblein designing matrix generators/languages for such a role. Itis then suggested that the approach most suited to general modelsis to design a language close to widely used mathematical notation.The facilities needed in such a language are discussed and theimplementation using the MAGIC (MAtrix Generator InstructionConvertor) language described.     

Complete flux scheme for parabolic singularly perturbed differential‐difference equations

In this study, we investigate the concept of the complete flux (CF) obtained as a solution to a local boundary value problem (BVP) for a given parabolic singularly perturbed differential‐difference equation (SPDDE) with modified source term to propose an efficient complete flux‐finite volume method (CF‐FVM) for parabolic SPDDE which is μ‐ and ?‐uniform method where μ, ? are shift and perturbation parameters, respectively. The proposed numerical method is shown to be consistent, stable, and convergent and has been successfully implemented on three test problems.     

Infinitesimal Perturbation Analysis: A Tool for Simulation

Perturbation analysis is a technique that expedites the process of performing experiments on discrete-event simulation models. This makes it possible to derive sensitivity estimates from one computer execution of a simulation model. Infinitesimal perturbation analysis (IPA) is one class of algorithms used in perturbation analysis. In this paper, the techniques and algorithms used in simulation to perform infinitesimal perturbation analysis are examined. Each algorithm is discussed in detail, with comments concerning implementation problems and examples with experimental results for serial transfer lines. The results of this paper show that for simple systems, IPA can be easily implemented in a general-purpose simulation language such as SIMAN. Unfortunately, for any given system, parameter or performance measure, the algorithm used to generate the gradient may vary. Additionally, algorithms for more complex classes of problems do not yet exist. This problem hampers the current possibility of incorporating IPA into general-purpose simulation languages.     

Understanding computer understanding of narrative text

This paper surveys recent successes in getting computers to understand human language by imbuing them with cultural knowledge and everyday common sense. The paper begins with a discussion of the centrality of language comprehension in giving computing machines their universality. Next, differences between formal programming languages currently understood by machines and properties of natural languages are discussed. The central problems of representing thought, encoding cultural knowledge, and generating inferences and cultural expectations are addressed within the context of the development of a number of computer programs dealing with narrative text. Finally, the paper ends with a discussion of the author's own computer program, BORIS, which extends the theory of language understanding and narrative comprehension in a number of directions. In particular, BORIS implements a theory of knowledge interactions, multiple perspectives, emotional reactions, parsing integrated with episodic memory, expectation failures, planning errors, and abstract narrative themes.     

A class of formal languages

We deal with languages that are classes of fully invariant congruences on free semigroups of finite rank. The question is posed as to whether a given fully invariant congruence coincides with a syntactic congruence of the language in question. If all classes of a given fully invariant congruence are rational languages, the corresponding variety is then said to be rational. A number of properties of rational varieties is established—in particular, we point to the way in which they are related to finite varieties. Translated fromAlgebra i Logika, Vol. 37, No. 4, pp. 478–492, July–August, 1998.     

Do there exist complete sets for promise classes?

In this paper we investigate the following two questions:

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