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We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for strict and non-strict cut-points of polynomially ambiguous commutative PFA remains undecidable, implying that the problem is undecidable when inputs are from a letter monotonic language. We show that the problem remains undecidable over a binary input alphabet when the input word is over a bounded language, in the noncommutative case. In doing so, we introduce a new technique based upon the Turakainen construction of a PFA from a Weighted Finite Automaton which can be used to generate PFA of lower dimensions and of sub-exponential ambiguity. We also study freeness/injectivity problems for polynomially ambiguous PFA and study the border of decidability and tractability for various cases. [ABSTRACT FROM AUTHOR]

The paper demonstrates the non-closure of the family of unambiguous linear languages (that is, those defined by unambiguous linear context-free grammars) under complementation. To be precise, a particular unambiguous linear grammar is presented, and it is proved that the complement of this language is not defined by any context-free grammar. This also constitutes an alternative proof for the result of Hibbard and Ullian ("The independence of inherent ambiguity from complementedness among context-free languages", JACM , 1966) on the non-closure of the unambiguous languages under complementation. [ABSTRACT FROM AUTHOR]

Phonetic categories have undefined edges, such that individual tokens that belong to different speech sound categories may occupy the same region in acoustic space. In continuous speech, there are multiple sources of top-down information (e.g., lexical, semantic) that help to resolve the identity of an ambiguous phoneme. Of interest is how these top-down constraints interact with ambiguity at the phonetic level. In the current fMRI study, participants passively listened to sentences that varied in semantic predictability and in the amount of naturally-occurring phonetic competition. The left middle frontal gyrus, angular gyrus, and anterior inferior frontal gyrus were sensitive to both semantic predictability and the degree of phonetic competition. Notably, greater phonetic competition within non-predictive contexts resulted in a negatively-graded neural response. We suggest that uncertainty at the phonetic-acoustic level interacts with uncertainty at the semantic level-perhaps due to a failure of the network to construct a coherent meaning. [ABSTRACT FROM AUTHOR]