Cost register automata (CRAs) are one-way finite automata whose transitions have the side effect that a register is set to the result of applying a state-dependent semiring operation to a pair of registers. Here it is shown that CRAs over the tropical semiring (N∪{∞},min,+) can simulate polynomial time computation, proving along the way that a naturally defined width-k circuit value problem ove...

In continuation of a previous works on semirings [5], in the present paper we introduce the notions of a strong ternary semiring (ST-semiring) (that is a ternary semirings with an additional condition called the left invertive law). We prove that many results obtained in [5] for semirings are still valid in the present case. We establish some relationships between the idempotents for both the a...

We associate with every commutative continuous semiring S and alphabet Σ a category whose objects are all sets and a morphism X → Y is determined by a function from X into the semiring of formal series S⟪(Y ⊎Σ) ⟫ of finite words over Y ⊎Σ, an X × Y -matrix over S⟪(Y ⊎Σ) ⟫, and a function from X into the continuous S⟪(Y ⊎Σ) ⟫-semimodule S⟪(Y ⊎Σ) ⟫ of series of ωwords over Y ⊎Σ. When S is also an...

Somatosensory event-related phase-ordered gamma oscillations (40-Hz) to electric painful standard stimuli under an odd-ball paradigm were analyzed in 13 high, 13 medium, and 12 low hypnotizable subjects during waking, hypnosis, and post-hypnosis conditions. During these conditions, subjects received a suggestion of Focused Analgesia to produce an obstructive hallucination of stimulus perception...

We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent gamma. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for gamma<3. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for gamma>3...