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Silva, Pedro V.
Silva, Pedro Mimoso

Silva, Pedro V.

Document

DOI: 10.4230/LIPIcs.STACS.2008.1321

A Mahler's theorem for functions from words to integers

Authors: Jean-Eric Pin and Pedro V. Silva

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract

In this paper, we prove an extension of Mahler's theorem, a celebrated result of $p$-adic analysis. Mahler's original result states that a function from $N$ to $Z$ is uniformly continuous for the $p$-adic metric $d_p$ if and only if it can be uniformly approximated by polynomial functions. We prove the same result for functions from $A^*$ to $Z$, where $d_p$ is now the profinite metric defined by $p$-groups (pro-$p$ metric).

Cite as

Jean-Eric Pin and Pedro V. Silva. A Mahler's theorem for functions from words to integers. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 585-596, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{pin_et_al:LIPIcs.STACS.2008.1321,
  author =	{Pin, Jean-Eric and Silva, Pedro V.},
  title =	{{A Mahler's theorem for functions from words to integers}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{585--596},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1321},
  URN =		{urn:nbn:de:0030-drops-13212},
  doi =		{10.4230/LIPIcs.STACS.2008.1321},
  annote =	{Keywords: \$p\$-adic topology, binomial coefficients, Mahler's theorem, \$p\$-group languages}
}

Silva, Pedro Mimoso

Document

DOI: 10.4230/OASIcs.SLATE.2020.4

BhTSL, Behavior Trees Specification and Processing

Authors: Miguel Oliveira, Pedro Mimoso Silva, Pedro Moura, José João Almeida, and Pedro Rangel Henriques

Published in: OASIcs, Volume 83, 9th Symposium on Languages, Applications and Technologies (SLATE 2020)

Abstract

In the context of game development, there is always the need for describing behaviors for various entities, whether NPCs or even the world itself. That need requires a formalism to describe properly such behaviors. As the gaming industry has been growing, many approaches were proposed. First, finite state machines were used and evolved to hierarchical state machines. As that formalism was not enough, a more powerful concept appeared. Instead of using states for describing behaviors, people started to use tasks. This concept was incorporated in behavior trees. This paper focuses in the specification and processing of Behavior Trees. A DSL designed for that purpose will be introduced. It will also be discussed a generator that produces LaTeX diagrams to document the trees, and a Python module to implement the behavior described. Additionally, a simulator will be presented. These achievements will be illustrated using a concrete game as a case study.

Cite as

Miguel Oliveira, Pedro Mimoso Silva, Pedro Moura, José João Almeida, and Pedro Rangel Henriques. BhTSL, Behavior Trees Specification and Processing. In 9th Symposium on Languages, Applications and Technologies (SLATE 2020). Open Access Series in Informatics (OASIcs), Volume 83, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{oliveira_et_al:OASIcs.SLATE.2020.4,
  author =	{Oliveira, Miguel and Silva, Pedro Mimoso and Moura, Pedro and Almeida, Jos\'{e} Jo\~{a}o and Henriques, Pedro Rangel},
  title =	{{BhTSL, Behavior Trees Specification and Processing}},
  booktitle =	{9th Symposium on Languages, Applications and Technologies (SLATE 2020)},
  pages =	{4:1--4:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-165-8},
  ISSN =	{2190-6807},
  year =	{2020},
  volume =	{83},
  editor =	{Sim\~{o}es, Alberto and Henriques, Pedro Rangel and Queir\'{o}s, Ricardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SLATE.2020.4},
  URN =		{urn:nbn:de:0030-drops-130174},
  doi =		{10.4230/OASIcs.SLATE.2020.4},
  annote =	{Keywords: Game development, Behavior trees (BT), NPC, DSL, Code generation}
}

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Documents authored by Silva, Pedro V.

Silva, Pedro V.

A Mahler's theorem for functions from words to integers

Abstract

Cite as

Silva, Pedro Mimoso

BhTSL, Behavior Trees Specification and Processing

Abstract

Cite as

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