東北大学 電気通信研究所 外山研究室では、NUEセミナーを開催しています。
テーマはプログラム理論や定理自動証明を中心に、
情報科学の理論的なさまざまな話題をとりあげています。
興味をおもちの方はどなたでもフラリと気楽におたちより下さい。
NUEセミナーの開催は **rewriting**、
**jssst-ppl**、 **logic-ml**、
**sonoteno**などのメーリングリストでアナウンスが行われています。

日時 | 2015年2月18日 |
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講演者 | Aart Middeldorp (University of Innsbruck) |

題目 | Conditional Complexity |

要旨 | In this talk we propose a notion of complexity for oriented conditional term rewrite systems. This notion is realistic in the sense that it measures not only successful computations but also partial computations that result in a failed rule application. A transformation to unconditional context-sensitive rewrite systems is presented which reflects this complexity notion, as well as a first technique to derive runtime and derivational complexity bounds for the latter. The talk is based on joint research with Cynthia Kop and Thomas Sternagel. |

日時 | 2013年10月29日 |
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講演者 | Vincent van Oostrom (Utrecht University) |

題目 | Z Syntax-Free Developments |

要旨 |
We introduce the Z-property for abstract rewriting systems, and
show that it can be used to prove confluence of several well-known
term rewrite systems (terminating or not, and overlapping or not), in
particular: - the applicative TRS for associativity: (xy)z -> x(yz); - the applicative TRS for self-distributivity: (xy)z -> xz(yz); - lambda-calculus with beta-reduction: (\x.M)N -> M[x:=N]. Turning to meta-theoretical properties, we first show that the Z-propery allows to recover the traditionally syntactically defined notion of (super)development/multistep in a syntax-free way. To that end, we show the equivalence between the Z-property and Takahashi's angle-property. Next, we showing that the Z-property not only entails confluence, but also the existence of a hyper-cofinal strategy. We conclude by presenting further (non-)examples of rewrite systems having the Z-property, and some open questions. |

日時 | 2013年5月23日 |
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講演者 | Irek Ulidowski (University of Leicester) |

題目 | Modelling of bonding with processes ad events |

要旨 | We introduce two forms of modelling of systems that consist of objects that are combined together by the means of bonds. In reaction systems for bonding we define how bonds are created and dissolved via reduction-style semantics. The usefulness of reaction systems is illustrated with examples taken from software engineering and biochemistry. We also introduce reversible event structures and define the notion of configuration. We then discuss how to give semantics of reaction systems for bonding in terms of reversible event structures. |

日時 | 2011年2月7日 |
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講演者 | Harald Zankl (University of Innsbruck) |

題目 | Labelings for Decreasing Diagrams |

要旨 | This talk is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We build on recent work (van Oostrom 2008), (Aoto 2010), and (Hirokawa and Middeldorp 2010) and study abstract criteria that allow to lexicographically combine labelings to show local diagrams decreasing. This approach has two immediate benefits. First, it allows to use labelings for linear rewrite systems also for left-linear ones, provided some mild conditions are satisfied. Second, it admits an incremental method for proving confluence which subsumes recent developments in automating decreasing diagrams. The techniques proposed in the paper have been implemented and experimental results demonstrate how, e.g., the rule labeling benefits from our contributions. |

日時 | 2008年8月27日 |
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講演者 | 酒井 正彦 (名古屋大学) |

題目 | シャローな項書換え系の最内停止性の決定可能性について |

要旨 | 変数の出現が深さ１以下に制限された項書換え系のクラスでは、最も 内側から計算を進める最内計算の停止性問題が決定可能であることを示す。こ の手法は依存対法に基づいているため、依存対プロセッサと呼ばれる停止性判 定ツールの構成手法と親和性が高く有効である。 |

日時 | 2008年8月4日 |
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講演者 | Aart Middeldorp (University of Innsbruck) |

題目 | Multi-Completion with Termination Tools |

要旨 | Knuth-Bendix completion is a well-known method for transforming equational theories into convergent rewrite systems. Traditional implementations of completion use a fixed reduction order to determine the orientation of rules. This restricts power and requires expertise of the user. In this talk we describe a new tool for performing completion with automatic termination tools. It is based on two ingredients: (1) the inference system for completion with multiple reduction orderings introduced by Kurihara and Kondo (1999) and (2) the inference system for completion with external termination provers proposed by Wehrman, Stump and Westbrook (2006) and implemented in the Slothrop system. Our tool can be used with any termination tool that satisfies certain minimal requirements. Preliminary experimental results show the potential of our tool. |

日時 | 2006年10月31日 |
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講演者 | Aart Middeldorp (University of Innsbruck) |

題目 | Predictive Labeling |

要旨 | Semantic labeling is a transformation technique for proving the termination of rewrite systems. The semantic part is given by a quasi-model of the rewrite rules. In this talk we present a variant of semantic labeling in which the quasi-model condition is only demanded for the usable rules induced by the labeling. Our variant is less powerful in theory but maybe more useful in practice. (This is a slight update of RTA 2006 talk). |

日時 | 2006年10月16日 |
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講演者 | Jean-Pierre Jouannaud (Ecole Polytechnique) |

題目 | Integrating Decision Procedures in the Calculus of Constructions |

要旨 |
It is commonly agreed that the success of future proof
assistants will rely on their ability to incorporate computations
within deductions in order to mimic the mathematician when replacing
the proof of a proposition P by the proof of an equivalent proposition
P' obtained from P thanks to possibly complex calculations. In this work, we investigate a new version of the calculus of constructions which incorporates arbitrary decision procedures into deductions via the conversion rule of the calculus. Besides the novelty of the problem itself in the context of the calculus of constructions, a major technical innovation of this work lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluency, strong normalization and decidability of proof-checking are all preserved. We also show in detail how a goal to be proved in the calculus of constructions is actually transformed into a goal in a decidable first-order theory. Based on this transformation, we are currently developping a new version of Coq implementing this calculus, taking linear arithmetic and the theory of lists as targets combined via Shostak's algorithm. |

日時 | 2006年5月24日 |
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講演者 | Jeroen Ketema (東北大) |

題目 | Infinitary Term Rewriting Systems |

要旨 |
Modelling lazy and stream based programming languages requires
the modelling of their infinite behaviour. Since Term Rewriting
Systems (TRSs) were developed to model finite behaviour, modelling the
infinite behaviour can be quite awkward. To alleviate this problem,
infinitary Term Rewriting Systems (iTRSs) were invented. In this talk I introduce the basic notions underlying the definition of iTRSs, i.e., infinite terms and infinite reductions. Time permitted, I thereafter show how to extend confluence, termination, normalisation, and modularity to iTRSs. For each of these notions I give examples of the failure of the most important results as they exist in the context of the usual TRSs and I hint at ways of partially recovering the results. |

[外山研究室] [電気通信研究所] [東北大学]

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