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Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this paper, we present a number of results that clarify the power of such machines and properties of the languages they define. The broad themes we focus on are as follows. We present results on the decidability and precise complexity of the emptiness, universality and language containment problems for such machines, thus answering questions central to the use of these models in formal verification. Next, we characterize the languages recognized by PBAs topologically, demonstrating that though general PBAs can recognize languages that are not regular, topologically the languages are as simple as \omega-regular languages. Finally, we introduce Hierarchical PBAs, which are syntactically restricted forms of PBAs that are tractable and capture exactly the class of \omega-regular languages.

Pulse Arrival Time (PAT) derived from Electrocardiogram (ECG) and Photoplethysmogram (PPG) for cuff-less Blood Pressure (BP) measurement has been a contemporary and widely accepted technique. However, the features extracted for it are conventionally from an isolated pulse of ECG and PPG signals. As a result, the estimated BP is intermittent. Objective: This paper presents feature extraction from each beat of ECG and PPG signals to make BP measurements uninterrupted. These features are extracted by employing Haar transformation to adaptively attenuate measurement noise and improve the fiducial point detection precision. Method: the use of only PAT feature as an independent variable leads to an inaccurate estimation of either Systolic Blood Pressure (SBP) or Diastolic Blood Pressure (DBP) or both. We propose the extraction of supplementary features that are highly correlated to physiological parameters. Concurrent data was collected as per the Association for the Advancement of Medical Instrumentation (AAMI) guidelines from 171 human subjects belonging to diverse age groups. An Adaptive Window Wavelet Transformation (AWWT) technique based on Haar wavelet transformation has been introduced to segregate pulses. Further, an algorithm based on log-linear regression analysis is developed to process extracted features from each beat to calculate BP. Results: The mean error of 0.43 and 0.20 mmHg, mean absolute error of 4.6 and 2.3 mmHg, and Standard deviation of 6.13 and 3.06 mmHg is achieved for SBP and DBP respectively. Conclusions: The features extracted are highly precise and evaluated BP values are as per the AAMI standards. Clinical Impact: This continuous real-time BP monitoring technique can be useful in the treatment of hypertensive and potential-hypertensive subjects.