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We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…
We introduce the notion of a risk-limiting financial auditing (RLFA): given $N$ transactions, the goal is to estimate the total misstated monetary fraction~($m^*$) to a given accuracy $\epsilon$, with confidence $1-\delta$. We do this by…
In probabilistic programming, the inference problem asks to determine a program's posterior distribution conditioned on its "observe" instructions. Inference is challenging, especially when exact rather than approximate results are…
We use a non-deterministic variant of storage types to develop a framework for the approximation of automata with storage. This framework is used to provide automata-theoretic views on the approximation of multiple context-free languages…
We present an algorithm to build an automaton from a rational expression. This approach introduces support for extended weighted expressions. Inspired by derived-term based algorithms, its core relies on a different construct, rational…
We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale's linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral…
Accurate estimation such as cost estimation, quality estimation and risk analysis is a major issue in management. We propose a patent pending soft computing framework to tackle this challenging problem. Our generic framework is independent…
Formal languages are in the core of models of computation and their behavior. A rich family of models for many classes of languages have been widely studied. Hyperproperties lift conventional trace-based languages from a set of execution…
We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic…
With the increasing power of computers and the rapid development of self-learning methodologies such as machine learning and artificial intelligence, the problem of constructing an automatic Financial Trading Systems (FTFs) becomes an…
We present a formal and constructive theory showing that probabilistic finite automata (PFAs) can be exactly simulated using symbolic feedforward neural networks. Our architecture represents state distributions as vectors and transitions as…
Automata play important roles in wide area of computing and the growth of multicores calls for their efficient parallel implementation. Though it is known in theory that we can perform the computation of a finite automaton in parallel by…
Families of deterministic finite automata (FDFA) represent regular $\omega$-languages through their ultimately periodic words (UP-words). An FDFA accepts pairs of words, where the first component corresponds to a prefix of the UP-word, and…
Nested weighted automata (NWA) present a robust and convenient automata-theoretic formalism for quantitative specifications. Previous works have considered NWA that processed input words only in the forward direction. It is natural to allow…
Financial structures such as securitisations, insurance contracts, and other hierarchical claims systems can be interpreted as deterministic allocation mechanisms acting on stochastic inflow processes. This paper develops a general…
We introduce notions of simulation between semiring-weighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo---hence soundness against language…
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
Financial models do not merely analyse markets, but actively shape them. This effect, known as performativity, describes how financial theories and the subsequent actions based on them influence market processes, by creating self-fulfilling…
Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared towards solving and modeling…