A cost recurrence describes an upper bound for the running time of a program in terms of the size of its input. Finding cost recurrences is a frequent intermediate step in complexity analysis, and this step requires an abstraction from data to data size. In this article, we use information contained in dependent types to achieve such an abstraction: Dependent ML (DML), a conservative extension of ML, provides dependent types that can be used to associate data with size information, thus describing a possible abstraction. We automatically extract cost recurrences from first-order DML programs, guiding the abstraction from data to data size with information contained in DML type derivations.

Cost recurrences for DML programs

Nested words, a model for recursive programs proposed by Alur and Madhusudan, have recently gained much interest. In this paper we introduce quantitative extensions and study nested word series which assign to nested words elements of a semiring. We show that regular nested word series coincide with series definable in weighted logics as introduced by Droste and Gastin. For this, we establish a connection between nested words and series-parallel-biposets. Applying our result, we obtain a characterization of algebraic formal power series in terms of weighted logics. This generalizes a result of Lautemann, Schwentick and Therien on context-free languages.

/pdf/weighted-logics-for-nested-words-and-algebraic-formal-power-3o8ysenpud.pdf

Weighted Logics for Nested Words and Algebraic Formal Power Series

Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related notion extends to more complex models, such as those developed for modeling distributed or timed behaviors.

https://hal.archives-ouvertes.fr/hal-00096619/document

Algebraic Recognizability of Languages

A Selective CPS Transformation

Review: C. C. Elgot, Decision Problems of Finite Automata Design and Related Arithmetics

We provide the basics of a 2-dimensional theory of automata on series-parallel biposets. We define recognizable, regular and rational sets of series-parallel biposets and study their relationship. Moreover, we relate these classes to languages of series-parallel biposets definable in monadic second-order logic.

/pdf/higher-dimensional-automata-17uoo2ovj4.pdf

Higher dimensional automata

/pdf/automata-on-series-parallel-biposets-2xjjuz8ftu.pdf

Automata on Series-Parallel Biposets

We provide the basics of a 2-dimensional theory of automata on seriesparallel biposets. We define recognizable, regular and rational sets of seriesparallel biposets and study their relationship. Moreover, we relate these classes to languages of series-parallel biposets definable in monadic second-order logic.

https://link.springer.com/content/pdf/10.1007%2F3-540-46011-X_18.pdf

Following from privacy requirements, new architecture solutions for personalized services are expected to emerge. This paper proposes a conceptual framework for designing privacy enabling service architectures, with a special emphasis on the mobile domain. The treatment of the subject is based on the principle of separating identity and profile information. Basic building blocks such as Identity Broker, Profile Broker, Contract Broker and Authenticator are identified and then put together in different ways resulting in variations on the architecture theme.

Privacy enhancing service architectures

Bisemigroups are algebras equipped with two independent associative operations. Labeled finite sp-biposets may serve as a possible representation of the elements of the free bisemigroups. For finite sp-biposets, an accepting device, called parenthesizing automaton, was introduced in [6], and it was proved that its expressive power is equivalent to both algebraic recognizability and monadic second order definability. In this paper, we show, how this concept of parenthesizing automaton can be generalized for infinite biposets in a way that the equivalence of regularity (defined by acceptance with automata), recognizability (defined by homomorphisms and finite ω-bisemigroups) and MSO-definability remains true.

Zoltán L. Németh

Papers

Higher dimensional automata

Automata on Series-Parallel Biposets

Automata on Series-Parallel Biposets

Privacy enhancing service architectures

Automata on infinite biposets