Global determinism of ternary semilattices

The global determinism of a ternary semigroup [Formula: see text] is the set of all nonempty subsets of [Formula: see text], denoted by [Formula: see text] equipped with the naturally defined multiplication. A class [Formula: see text] of ternary semigroups is said to be globally determined if any two members [Formula: see text] and [Formula: see text] of [Formula: see text] with isomorphic globals are themselves isomorphic i.e. [Formula: see text] implies that [Formula: see text] for any two ternary semigroups [Formula: see text] and [Formula: see text] in the class [Formula: see text]. In this paper, we mainly discuss that the class of all ternary semilattices are globally determined.

Quantum Mechanics and Global Determinism

It is proposed that certain features of quantum mechanics may be perspectival effects, which arise because experiments performed on locally accessible variables can only uncover a certain subset of the correlations exhibited by an underlying deterministic theory. This hypothesis is used to derive the no-signaling principle, thus resolving an open question regarding the apparently fine-tuned nature of quantum correlations. Some potential objections to this approach are then discussed and answered.Quanta 2018; 7: 40–53.

GLOBAL DETERMINISM OF CLIFFORD SEMIGROUPS

In this paper we shall give characterizations of the closed subsemigroups of a Clifford semigroup. Also, we shall show that the class of all Clifford semigroups satisfies the strong isomorphism property and so is globally determined. Thus the results obtained by Kobayashi [‘Semilattices are globally determined’, Semigroup Forum29 (1984), 217–222] and by Gould and Iskra [‘Globally determined classes of semigroups’ Semigroup Forum28 (1984), 1–11] are generalized.

ON DETERMINISTIC CD-SYSTEMS OF RESTARTING AUTOMATA

Three variants of determinism are introduced for CD-systems of restarting automata, called strict determinism, global determinism, and local determinism. In mode = 1 globally deterministic CD-systems of restarting automata are of the same expressive power as nonforgetting deterministic restarting automata of the same type, which corresponds to the situation for nondeterministic CD-systems. On the other hand, for the various types of restarting automata without auxiliary symbols, strictly deterministic CD-systems of restarting automata are strictly less expressive than the corresponding deterministic types of nonforgetting restarting automata. Further, globally deterministic CD-systems of restarting automata can be simulated by locally deterministic CD-systems of restarting automata of the same type. In fact, we conjecture that, for all types of restarting automata without auxiliary symbols, the latter are strictly more expressive than the former, but they are strictly less expressive than the corresponding nondeterministic CD-systems of restarting automata.