Alternation in Quantum Programming: From Superposition of Data to Superposition of Programs

We extract a novel quantum programming paradigm - superposition of programs - from the design idea of a popular class of quantum algorithms, namely quantum walk-based algorithms. The generality of this paradigm is guaranteed by the universality of quantum walks as a computational model. A new quantum programming language QGCL is then proposed to support the paradigm of superposition of programs. This language can be seen as a quantum extension of Dijkstra's GCL (Guarded Command Language). Surprisingly, alternation in GCL splits into two different notions in the quantum setting: classical alternation (of quantum programs) and quantum alternation, with the latter being introduced in QGCL for the first time. Quantum alternation is the key program construct for realizing the paradigm of superposition of programs. The denotational semantics of QGCL are defined by introducing a new mathematical tool called the guarded composition of operator-valued functions. Then the weakest precondition semantics of QGCL can straightforwardly derived. Another very useful program construct in realizing the quantum programming paradigm of superposition of programs, called quantum choice, can be easily defined in terms of quantum alternation. The relation between quantum choices and probabilistic choices is clarified through defining the notion of local variables. We derive a family of algebraic laws for QGCL programs that can be used in program verification, transformations and compilation. The expressive power of QGCL is illustrated by several examples where various variants and generalizations of quantum walks are conveniently expressed using quantum alternation and quantum choice. We believe that quantum programming with quantum alternation and choice will play an important role in further exploiting the power of quantum computing.Comment: arXiv admin note: substantial text overlap with arXiv:1209.437

The semantics of the native greek verb suffixes / Chariton Charitonidis

The aim of this paper is to give the semantic profile of the Greek verb-deriving suffixes -íz(o), -én(o), -év(o), -ón(o), -(i)áz(o), and -ín(o), with a special account of the ending -áo/-ó. The patterns presented are the result of an empirical analysis of data extracted from extended interviews conducted with 28 native Greek speakers in Athens, Greece in February 2009. In the first interview task the test persons were asked to force(=create) verbs by using the suffixes -ízo, -évo, -óno, -(i)ázo, and -íno and a variety of bases which conformed to the ontological distinctions made in Lieber (2004). In the second task the test persons were asked to evaluate three groups of forced verbs with a noun, an adjective, and an adverb, respectively, by using one (best/highly acceptable verb) to six (worst/unacceptable verb) points. In the third task nineteen established verb pairs with different suffixes and the ending -áo/-ó were presented. The test persons were asked to report whether there was some difference between them and what exactly this difference was. The differences reported were transformed into 16 alternations. In the fourth task 21 established verbs with different suffixes were presented. The test persons were asked to give the "opposite" or "near opposite" expression for each verb. The rationale behind this task was to arrive at the meaning of the suffixes through the semantics of the opposites. In the analysis Rochelle's Lieber's (2004) theoretical framework is used. The results of the analysis suggest (i) a sign-based treatment of affixes, (ii) a vertical preference structure in the semantic structure of the head suffixes which takes into account the semantic make-up of the bases, and (iii) the integration of socioexpressive meaning into verb structures

Towards the Formal Specification and Verification of Maple Programs

In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors in such programs w.r.t. their specifications by static analysis. This task is more complex for widely used computer algebra languages like Maple as these are fundamentally different from classical languages: they support non-standard types of objects such as symbols, unevaluated expressions and polynomials and require abstract computer algebraic concepts and objects such as rings and orderings etc. As a starting point we have defined and formalized a syntax, semantics, type system and specification language for MiniMaple

Morphological Cues for Lexical Semantics

Most natural language processing tasks require lexical semantic information. Automated acquisition of this information would thus increase the robustness and portability of NLP systems. This paper describes an acquisition method which makes use of fixed correspondences between derivational affixes and lexical semantic information. One advantage of this method, and of other methods that rely only on surface characteristics of language, is that the necessary input is currently available

Cinnamons: A Computation Model Underlying Control Network Programming

We give the easily recognizable name "cinnamon" and "cinnamon programming" to a new computation model intended to form a theoretical foundation for Control Network Programming (CNP). CNP has established itself as a programming paradigm combining declarative and imperative features, built-in search engine, powerful tools for search control that allow easy, intuitive, visual development of heuristic, nondeterministic, and randomized solutions. We define rigorously the syntax and semantics of the new model of computation, at the same time trying to keep clear the intuition behind and to include enough examples. The purposely simplified theoretical model is then compared to both WHILE-programs (thus demonstrating its Turing-completeness), and the "real" CNP. Finally, future research possibilities are mentioned that would eventually extend the cinnamon programming into the directions of nondeterminism, randomness, and fuzziness.Comment: 7th Intl Conf. on Computer Science, Engineering & Applications (ICCSEA 2017) September 23~24, 2017, Copenhagen, Denmar