منابع مشابه
Algebraic Notions of Termination
Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, Löb’s formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward and backward modal operators. To model infinite behaviours, idempotent semirings are extended to divergence ...
متن کاملAlgebraic Notions of Termination
Five algebraic notions of termination are formalised, analysed and compared: well-foundedness or Noetherity, Löb’s formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward and backward modal operators. To reason about infinite behaviour, semirings are extended to divergence semi...
متن کاملAlgebraic Notions of Non-Termination
We study and compare two notions of non-termination on idempotent semirings: infinite iteration and divergence. We determine them in various models and develop conditions for their coincidence. It turns out that divergence yields a simple and natural way of modelling infinite behaviour, whereas infinite iteration shows some anomalies.
متن کاملSome notions of D-algebraic geometry
When studying type-definable sets in closed Hasse fields, we observe a certain analogy with the case of algebraically closed fields. We show here in particular that connected type-definable groups can be described as “D-algebraic groups”, which is the natural equivalent for algebraic groups. However, many problems arise when we try to give a description of these geometric objects in the languag...
متن کاملTermination of Algebraic Rewriting with Inhibitors
We proceed with the study of termination properties in the double pushout approach to algebraic rewriting, and show a concrete termination criterion for rewriting systems with inhibitors. Inhibitors prevent elements in an algebra to participate in rule matches, so that termination depends only on whether new possibilities for matches are created. The notion of inhibitor can be extended to consi...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2011
ISSN: 1860-5974
DOI: 10.2168/lmcs-7(1:1)2011