Complete Symmetry in D2L Systems and Cellular Automata

We introduce completely symmetric D2L systems and cellular automata by means of an additional restriction on the corresponding symmetric devices. Then we show that completely symmetric D2L systems and cellular automata are still able to simulate Turing machine computations. As corollaries we obtain new characterizations of the recursively enumerable languages and of some space-bounded complexity classes

Binary Patterns in Binary Cube-Free Words: Avoidability and Growth

The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper bounds. Finally, a new example of a pattern-avoiding language of polynomial growth is given.Comment: 18 pages, 2 tables; submitted to RAIRO TIA (Special issue of Mons Days 2012

Dense-choice Counter Machines revisited

This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines, and we provide new undecidability and decidability results. Using the first-order additive mixed theory of reals and integers, we give a logical characterization of the sets of configurations reachable by reversal-bounded Dense-choice Counter Machines

Cultural variation in cognitive flexibility reveals diversity in the development of executive functions

Cognitive flexibility, the adaptation of representations and responses to new task demands, improves dramatically in early childhood. It is unclear, however, whether flexibility is a coherent, unitary cognitive trait, or is an emergent dimension of task-specific performance that varies across populations with divergent experiences. Three-to 5-year-old English-speaking U.S. children and Tswana-speaking South African children completed two distinct language-processing cognitive flexibility tests: the FIM-Animates, a word-learning test, and the 3DCCS, a rule-switching test. U.S. and South African children did not differ in word-learning flexibility but showed similar age-related increases. In contrast, U.S. preschoolers showed an age-related increase in rule-switching flexibility but South African children did not. Verbal recall explained additional variance in both tests but did not modulate the interaction between population sample (i.e., country) and task. We hypothesize that rule-switching flexibility might be more dependent upon particular kinds of cultural experiences, whereas word-learning flexibility is less cross-culturally variable

Remarks on separating words

The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem, consider some variations, and prove several new results