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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 global imperative to mitigate carbon emissions for sustainable development has spurred extensive research into economic, social, and energy-related factors. However, prior studies present a complex landscape, yielding mixed conclusions regarding the influence of geopolitical risk, natural resource rents, corrupt governance, and energy intensity. To untangle this ambiguity, we construct a research model grounded in the Environmental Kuznets Curve, employing panel data from 38 countries spanning 2002 to 2020. Employing panel quantile regression models, we directly assess the impact of identified factors. Our findings affirm the alignment between economic growth and carbon emissions, supporting the Environmental Kuznets Curve hypothesis. Notably, increased geopolitical risk and energy intensity correlate with heightened carbon emissions over time, while corruption governance and natural resource rents exhibit a mitigating effect. Additionally, our study explores the indirect impact of these factors using a panel threshold regression model. Results indicate a diminishing influence of economic growth on carbon emissions. Intriguingly, natural resource rents initially curtail, then amplify the connection between economic growth and carbon emissions. Conversely, rising energy intensity magnifies the relationship between economic expansion and carbon emissions. • Linear and nonlinear models were employed to explore the carbon emission influencing factors. • Explored the direct and indirect effects of geopolitical risk, natural resource rents, corruption and energy intensity on carbon emissions. • Natural resource rents, corruption governance in favour of lower carbon emissions, geopolitical risk and energy intensity in contrast. • Natural resource rents, corruption and geopolitical risks affect the relationship between economic growth and carbon emissions. [ABSTRACT FROM AUTHOR]

The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata. It is known that both problems are undecidable. We provide a more refined view of these problems in terms of the degree of ambiguity of probabilistic automata. We show that a gap version of the emptiness problem (known to be undecidable in general) becomes decidable for automata of polynomial ambiguity. We complement this positive result by showing that emptiness remains undecidable when restricted to automata of linear ambiguity. We then turn to finitely ambiguous automata and give a conditional decidability proof for containment in case one of the automata is assumed to be unambiguous. Part of our proof relies on the decidability of the theory of real exponentiation, proved, subject to Schanuel's Conjecture, by Macintyre and Wilkie. [ABSTRACT FROM AUTHOR]

• Young adults are sensitive to the reducibility of uncertainty during belief updating. • Updating processes are quasi-optimal and valence-dependent. • Neural responses in frontoparietal regions show valence-dependent recruitments. • Valence asymmetry at behavioral and neural levels is correlated. Selective use of new information is crucial for adaptive decision-making. Combining a gamble bidding task with assessing cortical responses using functional near-infrared spectroscopy (fNIRS), we investigated potential effects of information valence on behavioral and neural processes of belief and value updating during uncertainty reduction in young adults. By modeling changes in the participants' expressed subjective values using a Bayesian model, we dissociated processes of (i) updating beliefs about statistical properties of the gamble, (ii) updating values of a gamble based on new information about its winning probabilities, as well as (iii) expectancy violation. The results showed that participants used new information to update their beliefs and values about the gambles in a quasi-optimal manner, as reflected in the selective updating only in situations with reducible uncertainty. Furthermore, their updating was valence-dependent: information indicating an increase in winning probability was underweighted, whereas information about a decrease in winning probability was updated in good agreement with predictions of the Bayesian decision theory. Results of model-based and moderation analyses showed that this valence-dependent asymmetry was associated with a distinct contribution of expectancy violation, besides belief updating, to value updating after experiencing new positive information regarding winning probabilities. In line with the behavioral results, we replicated previous findings showing involvements of frontoparietal brain regions in the different components of updating. Furthermore, this study provided novel results suggesting a valence-dependent recruitment of brain regions. Individuals with stronger oxyhemoglobin responses during value updating was more in line with predictions of the Bayesian model while integrating new information that indicates an increase in winning probability. Taken together, this study provides first results showing expectancy violation as a contributing factor to sub-optimal valence-dependent updating during uncertainty reduction and suggests limitations of normative Bayesian decision theory. [ABSTRACT FROM AUTHOR]

• Positive judgments of ambiguous faces had strong fMRI activation in the CO network. • Accompanied by a second, late peak following final decision on emotional valence. • Supports the initial negativity hypothesis, showing positivity is a controlled process. • CO network activation reflects reporting of valence decision late in the trial. Cortical task control networks, including the cingulo-opercular (CO) network play a key role in decision-making across a variety of functional domains. In particular, the CO network functions in a performance reporting capacity that supports successful task performance, especially in response to errors and ambiguity. In two studies testing the contribution of the CO network to ambiguity processing, we presented a valence bias task in which masked clearly and ambiguously valenced emotional expressions were slowly revealed over several seconds. This slow reveal task design provides a window into the decision-making mechanisms as they unfold over the course of a trial. In the main study, the slow reveal task was administered to 32 young adults in the fMRI environment and BOLD time courses were extracted from regions of interest in three control networks. In a follow-up study, the task was administered to a larger, online sample (n = 81) using a more extended slow reveal design with additional unmasking frames. Positive judgments of surprised faces were uniquely accompanied by slower response times and strong, late activation in the CO network. These results support the initial negativity hypothesis, which posits that the default response to ambiguity is negative and positive judgments are associated with a more effortful controlled process, and additionally suggest that this controlled process is mediated by the CO network. Moreover, ambiguous trials were characterized by a second CO response at the end of the trial, firmly placing CO function late in the decision-making process. [ABSTRACT FROM AUTHOR]

In this work, we exploit the power of finite ambiguity for the complementation problem of Büchi automata by using reduced run directed acyclic graphs (DAGs) over infinite words, in which each vertex has at most one predecessor; these reduced run DAGs have only a finite number of infinite runs, thus obtaining the finite ambiguity in Büchi complementation. We show how to use this type of reduced run DAGs as a unified tool to optimize both rank-based and slice-based complementation constructions for Büchi automata with a finite degree of ambiguity. As a result, given a Büchi automaton with n states and a finite degree of ambiguity, the number of states in the complementary Büchi automaton constructed by the classical rank-based and slice-based complementation constructions can be improved from 2 O (n log ⁡ n) and O ((3 n) n) to O (6 n) ⊆ 2 O (n) and O (4 n) , respectively. We further show how to construct such reduced run DAGs for limit deterministic Büchi automata and obtain a specialized complementation algorithm, thus demonstrating the generality of the power of finite ambiguity. [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]

A morphism g is ambiguous with respect to a word u if there exists a second morphism h ≠ g such that g (u) = h (u). Otherwise g is unambiguous with respect to u. Thus unambiguous morphisms are those for which the structure of the morphism is preserved in the image. Ambiguity has so far been studied for morphisms of free monoids, where several characterisations exist for the set of words u permitting an (injective) unambiguous morphism. In the present paper, we consider ambiguity of morphisms of free groups, and consider possible analogies to the existing characterisations in the free monoid. While a direct generalisation results in a trivial situation where all morphisms are ambiguous, we discuss some natural and well-motivated reformulations, and provide a characterisation of words in a free group that permit a morphism which is "as unambiguous as possible". [ABSTRACT FROM AUTHOR]

Studies on decision-making under uncertainty have mainly focused on understanding preferences for either risk or ambiguity using standard lottery designs. However, people often face uncertainty that directly stems from interacting with other people, which may be processed differently from lottery-based uncertainty. Here, we substantially extend the investigation of uncertainty by examining a fourfold pattern of the sources and the types of uncertainty, assessing behavioral and neural responses to both risk and ambiguity across both social and non-social contexts. A key element in our research design was to control for participants' naturally occurring social beliefs, and taking these a priori beliefs into account allow us to elicit individual preferences in accordance with economic approaches that stress the dynamics of ambiguity preference as a function of underlying likelihoods. Using this design, we find a behavioral main effect of ambiguity aversion, with increasing ambiguity aversion as a function of higher beliefs regarding the likelihood of reciprocity, and related neural activity in the right IPS. This brain region was primarily involved when participants experienced lottery-based uncertainty as opposed to social uncertainty. However, we found that the right IFG was more involved when participants made decisions under social, as compared to non-social, uncertainty. Overall, therefore, the IPS may activate an analytic mindset, which might resonate more with a lottery than a social context, whereas the IFG is engaged when the context requires players to resolve uncertainty, such as unraveling the intentions behind the choice of another person. [ABSTRACT FROM AUTHOR]

Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many algorithmic questions are undecidable. In this work we focus on the emptiness problem (and its variant the value problem), which asks whether a given probabilistic automaton accepts some word with probability greater than a given threshold. We consider finitely ambiguous probabilistic automata. Our main contributions are to construct efficient algorithms for analysing finitely ambiguous probabilistic automata through a reduction to a multi-objective optimisation problem called the stochastic path problem. We obtain a polynomial time algorithm for approximating the value of probabilistic automata of fixed ambiguity and a quasi-polynomial time algorithm for the emptiness problem for 2-ambiguous probabilistic automata. We complement these positive results by an inapproximability result stating that the value of finitely ambiguous probabilistic automata cannot be approximated unless P = NP. [ABSTRACT FROM AUTHOR]

An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is finitely (respectively, countably) ambiguous if for every input it has at most finitely (respectively, countably) many accepting computations. An automaton is boundedly ambiguous if there is k ∈ N , such that for every input it has at most k accepting computations. We consider nondeterministic Büchi automata (NBA) over infinite trees and prove that it is decidable in polynomial time, whether an automaton is unambiguous, boundedly ambiguous, finitely ambiguous, or countably ambiguous. [ABSTRACT FROM AUTHOR]

Risk and ambiguity are inherent in virtually all human decision-making. Risk refers to a situation in which we know the precise probability of potential outcomes of each option, whereas ambiguity refers to a situation in which outcome probabilities are not known. A large body of research has shown that individuals prefer known risks to ambiguity, a phenomenon known as ambiguity aversion. One heated debate concerns whether risky and ambiguous decisions rely on the same or distinct neural circuits. In the current meta-analyses, we integrated the results of neuroimaging research on decision-making under risk (n = 69) and ambiguity (n = 31). Our results showed that both processing of risk and ambiguity showed convergence in anterior insula, indicating a key role of anterior insula in encoding uncertainty. Risk additionally engaged dorsomedial prefrontal cortex (dmPFC) and ventral striatum, whereas ambiguity specifically recruited the dorsolateral prefrontal cortex (dlPFC), inferior parietal lobe (IPL) and right anterior insula. Our findings demonstrate overlapping and distinct neural substrates underlying different types of uncertainty, guiding future neuroimaging research on risk-taking and ambiguity aversion. [ABSTRACT FROM AUTHOR]

Neural Referring Expression Generation (REG) models have shown promising results in generating expressions which uniquely describe visual objects. However, current REG models still lack the ability to produce diverse and unambiguous referring expressions (REs). To address the lack of diversity, we propose generating a set of diverse REs, rather than one-shot REs. To reduce the ambiguity of referring expressions, we directly optimise non-differentiable test metrics using reinforcement learning (RL), and we show that our approaches achieve better results under multiple different settings. Specifically, we initially present a novel RL approach to REG training, which instead of drawing one sample per input, it averages over multiple samples to normalize the reward during RL training. Secondly, we present an innovative REG model that utilizes an object attention mechanism that explicitly incorporates information about the target object and is optimised using our proposed RL approach. Thirdly, we propose a novel transformer model optimised with RL that exploits different levels of visual information. Our human evaluation demonstrates the effectiveness of this model, where we improve the state-of-the-art results in RefCOCO testA and testB in terms of task success from 76.95 % to 81.66 % and from 78.10 % to 83.33 % respectively. While in RefCOCO+ testA we show improvements from 58.85 % to 83.33 %. Finally, we present a thorough comparison of diverse decoding strategies (sampling and maximisation-based) and how they control the trade-off between the quality and diversity. [ABSTRACT FROM AUTHOR]