64 research outputs found
On 3-Coloring Circle Graphs
Given a graph with a fixed vertex order , one obtains a circle
graph whose vertices are the edges of and where two such edges are
adjacent if and only if their endpoints are pairwise distinct and alternate in
. Therefore, the problem of determining whether has a -page book
embedding with spine order is equivalent to deciding whether can be
colored with colors. Finding a -coloring for a circle graph is known to
be NP-complete for and trivial for . For , Unger
(1992) claims an efficient algorithm that finds a 3-coloring in
time, if it exists. Given a circle graph , Unger's algorithm (1) constructs
a 3-\textsc{Sat} formula that is satisfiable if and only if admits a
3-coloring and (2) solves by a backtracking strategy that relies on the
structure imposed by the circle graph. However, the extended abstract misses
several details and Unger refers to his PhD thesis (in German) for details. In
this paper we argue that Unger's algorithm for 3-coloring circle graphs is not
correct and that 3-coloring circle graphs should be considered as an open
problem. We show that step (1) of Unger's algorithm is incorrect by exhibiting
a circle graph whose formula is satisfiable but that is not 3-colorable.
We further show that Unger's backtracking strategy for solving in step
(2) may produce incorrect results and give empirical evidence that it exhibits
a runtime behaviour that is not consistent with the claimed running time.Comment: Appears in the Proceedings of the 31st International Symposium on
Graph Drawing and Network Visualization (GD 2023
Modelling and Simulation of Asynchronous Real-Time Systems using Timed Rebeca
In this paper we propose an extension of the Rebeca language that can be used
to model distributed and asynchronous systems with timing constraints. We
provide the formal semantics of the language using Structural Operational
Semantics, and show its expressiveness by means of examples. We developed a
tool for automated translation from timed Rebeca to the Erlang language, which
provides a first implementation of timed Rebeca. We can use the tool to set the
parameters of timed Rebeca models, which represent the environment and
component variables, and use McErlang to run multiple simulations for different
settings. Timed Rebeca restricts the modeller to a pure asynchronous
actor-based paradigm, where the structure of the model represents the service
oriented architecture, while the computational model matches the network
infrastructure. Simulation is shown to be an effective analysis support,
specially where model checking faces almost immediate state explosion in an
asynchronous setting.Comment: In Proceedings FOCLASA 2011, arXiv:1107.584
Token-passing nets for functional languages
Proceedings of the 7th International Workshop on Reduction Strategies in Rewriting and Programming (WRS 2007)Token-passing nets were proposed by Sinot as a simple mechanism for encoding evaluation strategies for the λ-calculus in interaction nets. This work extends token-passing nets to cover a typed functional language equipped with structured types and unrestricted recursion. The resulting interaction system is derived systematically from the chosen big-step operational semantics. Along the way, we actually characterize and discuss several design decisions of token-passing nets and extend them in order to achieve simpler interaction net systems with a higher degree of embedded parallelism.Fundação para a Ciência e a Tecnologia (FCT
A Tool for Describing and Checking Natural Semantics Definitions of Programming Languages
Many universities have courses and projects revolving around compiler or
interpreter implementation as part of their degree programmes in computer
science. In such teaching activities, tool support can be highly beneficial.
While there are already several tools for assisting with development of the
front end of compilers, tool support tapers off towards the back end, or
requires more background experience than is expected of undergraduate students.
Structural operational semantics is a useful and mathematically simple
formalism for specifying the behaviour of programs and a specification lends
itself well to implementation; in particular big-step or natural semantics is
often a useful and simple approach. However, many students struggle with
learning the notation and often come up with ill-defined and meaningless
attempts at defining a structural operational semantics. A survey shows that
students working on programming language projects feel that tool support is
lacking and would be useful.
Many of these problems encountered when developing a semantic definition are
similar to problems encountered in programming, in particular ones that are
essentially the result of type errors.
We present a pedagogical metalanguage based on natural semantics, and its
implementation, as an attempt to marry two notions: a syntax similar to
textbook notation for natural semantics on the one hand, and automatic
verification of some correctness properties on the other by means of a strong
type discipline. The metalanguage and the tool provide the facilities for
writing and executing specifications as a form of programming. The user can
check that the specification is not meaningless as well as execute programs, if
the specification makes sense.Comment: In Proceedings FROM 2022, arXiv:2209.0920
Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting
At the core of the quest for a logic for Ptime is a mismatch between algorithms making arbitrary choices and isomorphism-invariant logics. One approach to tackle this problem is witnessed symmetric choice. It allows for choices from definable orbits certified by definable witnessing automorphisms.
We consider the extension of fixed-point logic with counting (IFPC) with witnessed symmetric choice (IFPC+WSC) and a further extension with an interpretation operator (IFPC+WSC+I). The latter operator evaluates a subformula in the structure defined by an interpretation. When similarly extending pure fixed-point logic (IFP), IFP+WSC+I simulates counting which IFP+WSC fails to do. For IFPC+WSC, it is unknown whether the interpretation operator increases expressiveness and thus allows studying the relation between WSC and interpretations beyond counting.
In this paper, we separate IFPC+WSC from IFPC+WSC+I by showing that IFPC+WSC is not closed under FO-interpretations. By the same argument, we answer an open question of Dawar and Richerby regarding non-witnessed symmetric choice in IFP. Additionally, we prove that nesting WSC-operators increases the expressiveness using the so-called CFI graphs. We show that if IFPC+WSC+I canonizes a particular class of base graphs, then it also canonizes the corresponding CFI graphs. This differs from various other logics, where CFI graphs provide difficult instances
KGRAM: une machine abstraite de graphes de connaissance
National audienceCet article présente la machine abstraite de graphes de connaissance KGRAM qui unifie les notions d'homomorphisme de graphe et de calcul de re-quêtes telles que celles du langage SPARQL sur des données RDF. KGRAM implémente un ensemble extensible d'expressions qui définissent une famille de langages abstraits d'interrogation de graphes, GRAAL. Nous décrivons la sé-mantique dynamique de GRAAL en Sémantique Naturelle et nous présentons la machine abstraite KGRAM conçue comme l'interprète de GRAAL, qui implé-mente les règles de sémantique naturelle du langage
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