7,674 research outputs found
Synchronous products of rewrite systems (extended version)
We present and formalize a concept of synchronous product for rewrite systems, and also a corresponding concept for general transition systems, used as semantics for the former. A series of examples shows their practical usefulness: for the strategic control of systems, and for modular specification and verification
The Parametric Ordinal-Recursive Complexity of Post Embedding Problems
Post Embedding Problems are a family of decision problems based on the
interaction of a rational relation with the subword embedding ordering, and are
used in the literature to prove non multiply-recursive complexity lower bounds.
We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove
parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page
Colored operads, series on colored operads, and combinatorial generating systems
We introduce bud generating systems, which are used for combinatorial
generation. They specify sets of various kinds of combinatorial objects, called
languages. They can emulate context-free grammars, regular tree grammars, and
synchronous grammars, allowing us to work with all these generating systems in
a unified way. The theory of bud generating systems uses colored operads.
Indeed, an object is generated by a bud generating system if it satisfies a
certain equation in a colored operad. To compute the generating series of the
languages of bud generating systems, we introduce formal power series on
colored operads and several operations on these. Series on colored operads are
crucial to express the languages specified by bud generating systems and allow
us to enumerate combinatorial objects with respect to some statistics. Some
examples of bud generating systems are constructed; in particular to specify
some sorts of balanced trees and to obtain recursive formulas enumerating
these.Comment: 48 page
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