In this paper we prove that, if V is a κ-tame pseudovariety which satisfies the pseudoidentity xyz = xyz, then the pseudovariety join LSl∨V is also κ-tame. Here, LSl denotes the pseudovariety of local semilattices and κ denotes the implicit signature consisting of the multiplication and the (ω − 1)-power. As a consequence, we deduce that LSl ∨V is decidable. In particular the joins LSl ∨ Ab, LS...

The effectiveness of reputation systems for peer-to-peer resource-sharing networks is largely dependent on the reliability of the identities used by peers in the network. Much debate has centered around how closely one’s pseudoidentity in the network should be tied to their real-world identity, and how that identity is protected from malicious spoofing. In this paper we investigate the cost in ...

After developing a theory of implicit operations and proving an analogue of Reiterman's theorem for categories, this paper addresses two complementary questions for semidirect products and two-sided semidirect products of pseudovarieties of semigroups: to determine when a pseudoidentity is valid in it, and to nd a basis of pseudoidentities. The rst question involves looking into the structure o...

In this paper, we establish several decidability results for pseudovariety joins of the form V ∨ W, where V is a subpseudovariety of J or the pseudovariety R. Here, J (resp. R) denotes the pseudovariety of all J-trivial (resp. R-trivial) semigroups. In particular, we show that the pseudovariety V ∨ W is (completely) κ-tame when V is a subpseudovariety of J with decidable κ-word problem and W is...