Estimation over Communication Networks: Performance Bounds and Achievability Results

This paper considers the problem of estimation over communication networks. Suppose a sensor is taking measurements of a dynamic process. However the process needs to be estimated at a remote location connected to the sensor through a network of communication links that drop packets stochastically. We provide a framework for computing the optimal performance in the sense of expected error covariance. Using this framework we characterize the dependency of the performance on the topology of the network and the packet dropping process. For independent and memoryless packet dropping processes we find the steady-state error for some classes of networks and obtain lower and upper bounds for the performance of a general network. Finally we find a necessary and sufficient condition for the stability of the estimate error covariance for general networks with spatially correlated and Markov type dropping process. This interesting condition has a max-cut interpretation

Annotating large lattices with the exact word error

The acoustic model in modern speech recognisers is trained discriminatively, for example with the minimum Bayes risk. This criterion is hard to compute exactly, so that it is normally approximated by a criterion that uses fixed alignments of lattice arcs. This approximation becomes particularly problematic with new types of acoustic models that require flexible alignments. It would be best to annotate lattices with the risk measure of interest, the exact word error. However, the algorithm for this uses finite-state automaton determinisation, which has exponential complexity and runs out of memory for large lattices. This paper introduces a novel method for determinising and minimising finite-state automata incrementally. Since it uses less memory, it can be applied to larger lattices.This work was supported by EPSRC Project EP/I006583/1 (Generative Kernels and Score Spaces for Classification of Speech) within the Global Uncertainties Programme and by a Google Research Award.This is the author accepted manuscript. The final version is available from ISCA via http://www.isca-speech.org/archive/interspeech_2015/i15_2625.htm

Optimal energetic paths for electric cars

A weighted directed graph $G=(V,A,c)$, where $A\subseteq V\times V$ and $c:A\to R$, describes a road network in which an electric car can roam. An arc $uv$ models a road segment connecting the two vertices $u$ and $v$. The cost $c(uv)$ of an arc $uv$ is the amount of energy the car needs to traverse the arc. This amount may be positive, zero or negative. To make the problem realistic, we assume there are no negative cycles. The car has a battery that can store up to $B$ units of energy. It can traverse an arc $uv\in A$ only if it is at $u$ and the charge $b$ in its battery satisfies $b\ge c(uv)$. If it traverses the arc, it reaches $v$ with a charge of $\min(b-c(uv),B)$. Arcs with positive costs deplete the battery, arcs with negative costs charge the battery, but not above its capacity of $B$. Given $s,t\in V$, can the car travel from $s$ to $t$, starting at $s$ with an initial charge $b$, where $0\le b\le B$? If so, what is the maximum charge with which the car can reach $t$? Equivalently, what is the smallest $\delta_{B,b}(s,t)$ such that the car can reach $t$ with a charge of $b-\delta_{B,b}(s,t)$, and which path should the car follow to achieve this? We refer to $\delta_{B,b}(s,t)$ as the energetic cost of traveling from $s$ to $t$. We let $\delta_{B,b}(s,t)=\infty$ if the car cannot travel from $s$ to $t$ starting with an initial charge of $b$. The problem of computing energetic costs is a strict generalization of the standard shortest paths problem. We show that the single-source minimum energetic paths problem can be solved using simple, but subtle, adaptations of the Bellman-Ford and Dijkstra algorithms. To make Dijkstra's algorithm work in the presence of negative arcs, but no negative cycles, we use a variant of the $A^*$ search heuristic. These results are explicit or implicit in some previous papers. We provide a simpler and unified description of these algorithms.Comment: 11 page

Nested Weighted Limit-Average Automata of Bounded Width

While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness

Weighted Relational Models for Mobility

We investigate operational and denotational semantics for computational and concurrent systems with mobile names which capture their computational properties. For example, various properties of fixed networks, such as shortest or longest path, transition probabilities, and secure data flows, correspond to the ``sum\u27\u27 in a semiring of the weights of paths through the network: we aim to model networks with a dynamic topology in a similar way. Alongside rich computational formalisms such as the lambda-calculus, these can be represented as terms in a calculus of solos with weights from a complete semiring $R$, so that reduction associates a weight in R to each reduction path. Taking inspiration from differential nets, we develop a denotational semantics for this calculus in the category of sets and R-weighted relations, based on its differential and compact-closed structure, but giving a simple, syntax-independent representation of terms as matrices over R. We show that this corresponds to the sum in R of the values associated to its independent reduction paths, and that our semantics is fully abstract with respect to the observational equivalence induced by sum-of-paths evaluation

Bidirectional Nested Weighted Automata

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 the automata to process input words backwards as well, for example, to measure the maximal or average time between a response and the preceding request. We therefore introduce and study bidirectional NWA that can process input words in both directions. First, we show that bidirectional NWA can express interesting quantitative properties that are not expressible by forward-only NWA. Second, for the fundamental decision problems of emptiness and universality, we establish decidability and complexity results for the new framework which match the best-known results for the special case of forward-only NWA. Thus, for NWA, the increased expressiveness of bidirectionality is achieved at no additional computational complexity. This is in stark contrast to the unweighted case, where bidirectional finite automata are no more expressive but exponentially more succinct than their forward-only counterparts