GROUPS THAT DO AND DO NOT HAVE GROWING CONTEXT-SENSITIVE WORD PROBLEM

Groups that do and do not Have Growing Context-Sensitive Word Problem

We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and Shapiro in [6]). We generalize results of [6] to find many examples of groups not admitting non-deterministic Cannon's algorithms. This adds to the examples of Kambi...

Church-Rosser Groups and Growing Context-Sensitive Groups

A finitely generated group is called a Church-Rosser group (growing contextsensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the ChurchRosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free language...

Dark Chocolate and Metabolic Syndrome; Do Polyphenols All that Matter?

Apes have culture but may not know that they do

There is good evidence that some ape behaviors can be transmitted socially and that this can lead to group-specific traditions. However, many consider animal traditions, including those in great apes, to be fundamentally different from human cultures, largely because of lack of evidence for cumulative processes and normative conformity, but perhaps also because current research on ape culture i...

Random groups do not split

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on simplicial trees. This implies that their Gromov boundaries, defined at density less than 1 2 , are Menger curves. Mathematics Subject Classification (2000) 20F65 · 20F67 · 20E08