Prakash Panangaden

Prakash Panangaden
McGill University | McGill · School of Computer Science

About

243
Publications
15,212
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7,511
Citations
Citations since 2016
22 Research Items
1986 Citations
2016201720182019202020212022050100150200250300
2016201720182019202020212022050100150200250300
2016201720182019202020212022050100150200250300
2016201720182019202020212022050100150200250300
Additional affiliations
June 1990 - present
McGill University
Position
  • Professor (Full)
August 1985 - December 1989
Cornell University
Position
  • Professor (Assistant)

Publications

Publications (243)
Preprint
ion has been widely studied as a way to improve the efficiency and generalization of reinforcement learning algorithms. In this paper, we study abstraction in the continuous-control setting. We extend the definition of MDP homomorphisms to encompass continuous actions in continuous state spaces. We derive a policy gradient theorem on the abstract M...
Preprint
We study the approximate minimization problem of weighted finite automata (WFAs): given a WFA, we want to compute its optimal approximation when restricted to a given size. We reformulate the problem as a rank-minimization task in the spectral norm, and propose a framework to apply Adamyan-Arov-Krein (AAK) theory to the approximation problem. This...
Preprint
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We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of equality has to be interpreted in the Boolean algebra and when we say that an equation is valid in the model we m...
Preprint
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We develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras. Unlike previous related work about fixed-points in metric spaces, we are working with the notion of approximate equality rather than exact equality. The result is a novel theory of fixed points which can not only pro...
Preprint
Full-text available
In this paper we study the approximate minimization problem for language modelling. We assume we are given some language model as a black box. The objective is to obtain a weighted finite automaton (WFA) that fits within a given size constraint and which mimics the behaviour of the original model while minimizing some notion of distance between the...
Preprint
We present a new behavioural distance over the state space of a Markov decision process, and demonstrate the use of this distance as an effective means of shaping the learnt representations of deep reinforcement learning agents. While existing notions of state similarity are typically difficult to learn at scale due to high computational cost and l...
Preprint
Full-text available
We address the approximate minimization problem for weighted finite automata (WFAs) over a one-letter alphabet: to compute the best possible approximation of a WFA given a bound on the number of states. This work is grounded in Adamyan-Arov-Krein Approximation theory, a remarkable collection of results on the approximation of Hankel operators. In a...
Preprint
Full-text available
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs, but for the first time admit an adequacy theorem relating the operational and denotational views. This resolves...
Article
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 properties of sets of linear operators. In particular, the joint spectral radius of the transition matrices of W...
Preprint
Full-text available
Stone-type dualities provide a powerful mathematical framework for studying properties of logical systems. They have recently been fruitfully explored in understanding minimisation of various types of automata. In Bezhanishvili et al. (2012), a dual equivalence between a category of coalgebras and a category of algebras was used to explain minimisa...
Conference Paper
Markov processes are a fundamental model of probabilistic transition systems and are the underlying semantics of probabilistic programs. We give an algebraic axiomatisation of Markov processes using the framework of quantitative equational logic introduced in [13]. We present the theory in a structured way using work of Hyland et al. [9] on combini...
Conference Paper
The ordinary untyped λ-calculus has a λ-theoretic model proposed in two related forms by Scott and Plotkin in the 1970s. Recently Scott showed how to introduce probability by extending these models with random variables. However, to reason about correctness and to add further features, it is useful to reinterpret the construction in a higher-order...
Article
Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by the same authors in a related paper presented at LICS 2016. These algebras provide the mathematical foundation for metric semantics of probabilistic, stochastic and other quantitative systems. This paper considers the issue of ax...
Article
We present an algebraic account of the Wasserstein distances $W_p$ on complete metric spaces. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in $p$, for algebras over metric spaces equipped with probabilistic choice operations. The axioms say that the opera...
Article
The present paper uses spectral theory of linear operators to construct approximately minimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the SVD decomposition of infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising fr...
Article
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 properties of sets of linear operators. In particular, the joint spectral radius of the transition matrices of W...
Conference Paper
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed by rationals: a = ϵ b which we think of as saying that "a is approximately equal to b up to an error of ϵ ". We have 4 interesting examples where we have a quantitative equational theory whose free algebr...
Article
Full-text available
We propose a notion of quantum control in a quantum programming language which permits the superposition of finitely many quantum operations without performing a measurement. This notion takes the form of a conditional construct similar to the IF statement in classical programming languages. We show that adding such a quantum IF statement to the QP...
Article
We provide a novel, flexible, iterative refinement algorithm to automatically construct an approximate statespace representation for Markov Decision Processes (MDPs). Our approach leverages bisimulation metrics, which have been used in prior work to generate features to represent the state space of MDPs. We address a drawback of this approach, whic...
Article
We provide a novel, flexible, iterative refinement algorithm to automatically construct an approximate statespace representation for Markov Decision Processes (MDPs). Our approach leverages bisimulation metrics, which have been used in prior work to generate features to represent the state space of MDPs.We address a drawback of this approach, which...
Article
Full-text available
We study the problem of constructing approximations to a weighted automaton. Weighted finite automata (WFA) are closely related to the theory of rational series. A rational series is a function from strings to real numbers that can be computed by a finite WFA. Among others, this includes probability distributions generated by hidden Markov models a...
Article
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This volume contains the proceedings of the 11th International Workshop on Quantum Physics and Logic (QPL 2014), which was held from the 4th to the 6th of June, 2014, at Kyoto University, Japan. The goal of the QPL workshop series is to bring together researchers working on mathematical foundations of quantum physics, quantum computing and spatio-t...
Article
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We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the way to developing theories of approximate reasoning for...
Article
Glynn Winskel has had enormous influence on the study of causal structure in computer science. In this brief note, I discuss analogous concepts in relativity where also causality plays a fundamental role. I discuss spacetime structure in a series of layers and emphasize the role of causal structure. I close with some comparisons between causality i...
Article
This volume contains the proceedings of the ninth workshop on Quantum Physics and Logic (QPL2012) which took place in Brussels from the 10th to the 12th of October 2012. QPL2012 brought together researchers working on mathematical foundations of quantum physics, quantum computing, and spatio-temporal causal structures. The particular focus was on t...
Article
We give a new presentation of Brzozowski's algorithm to minimize finite automata using elementary facts from universal algebra and coalgebra and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to fur...
Conference Paper
Full-text available
Functional Reactive Programming (FRP) models reactive systems with events and signals, which have previously been observed to correspond to the "eventually" and "always" modalities of linear temporal logic (LTL). In this paper, we define a constructive variant of LTL with least fixed point and greatest fixed point operators in the spirit of the mod...
Conference Paper
In this paper we present Hilbert-style axiomatizations for three logics for reasoning about continuous-space Markov processes (MPs): (i) a logic for MPs defined for probability distributions on measurable state spaces, (ii) a logic for MPs defined for sub-probability distributions and (iii) a logic defined for arbitrary distributions. These logics...
Article
Full-text available
We analyze the transformation of the polarization of a photon propagating along an arbitrary null geodesic in Kerr geometry. The motivation comes from the problem of an observer trying to communicate quantum information to another observer in Kerr spacetime by transmitting polarized photons. It is essential that the observers understand the relatio...
Conference Paper
I give a brief introduction to Stone duality and then survey a number of duality theories that arise in logic and computer science. I mention some more unfamiliar dualities at the end which may be of importance to emerging fields within computer science.
Conference Paper
We define Aumann algebras, an algebraic analog of probabilistic modal logic. An Aumann algebra consists of a Boolean algebra with operators modeling probabilistic transitions. We prove a Stone-type duality theorem between countable Aumann algebras and countably-generated continuous-space Markov processes. Our results subsume existing results on com...
Article
The notion of a particle in quantum field theory is dependent on the observer. This fundamental ambiguity in the definition of what seems a basic “objectively” observable concept is unsettling. In this short note I will survey the basics of field quantization and then discuss the Unruh effect which illustrates this phenomenon. I will describe an ab...
Book
This Festschrift volume, published in honor of Samson Abramsky, contains contributions written by some of his colleagues, former students, and friends. In celebration of the 60th birthday of Samson Abramsky, a conference was held in Oxford, UK, during May 28-30, 2010. The papers in this volume represent his manifold contributions to semantics, logi...
Article
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We develop a game semantics for process algebra with two interacting agents. The purpose of our semantics is to make manifest the role of knowledge and information ow in the interactions between agents and to control the information available to interacting agents. We dene games and strategies on process algebras, so that two agents interacting acc...
Conference Paper
Full-text available
We study the problem of determining approximate equivalences in Markov Decision Processes with rewards using bisimulation metrics. We provide an extension of the framework previously introduced in Ferns et al. (2004), which computes iteratively improving approximations to bisimulation metrics using exhaustive pairwise state comparisons. The similar...
Conference Paper
Full-text available
We introduce spatial and epistemic process calculi for reasoning about spatial information and knowledge distributed among the agents of a system. We introduce domain-theoretical structures to represent spatial and epistemic information. We provide operational and denotational techniques for reasoning about the potentially infinite behaviour of spa...
Conference Paper
We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the...
Article
Full-text available
Universal algebra is often known within computer science in the guise of algebraic specification or equational logic. In 1963, it was given a category theoretic characterisation in terms of what are now called Lawvere theories. Unlike operations and ...
Conference Paper
We develop a fusion of logical and metrical principles for reasoning about Markov processes. More precisely, we lift metrics from processes to sets of processes satisfying a formula and explore how the satisfaction relation behaves as sequences of processes and sequences of formulas approach limits. A key new concept is dynamically-continuous metri...
Article
Measurement-based quantum computation (MBQC) has emerged as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model that takes unitary operations as fundamental. Among measurement-based quantum computation methods the recently introdu...
Article
Full-text available
We present metrics for measuring the similarity of states in a finite Markov decision process (MDP). The formulation of our metrics is based on the notion of bisimulation for MDPs, with an aim towards solving discounted infinite horizon reinforcement learning tasks. Such metrics can be used to aggregate states, as well as to better structure other...
Article
Full-text available
We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of bisimulation for MDPs, and are suitable for use in MDP approximation. We show that the optimal value function associated...
Article
Full-text available
A popular approach to solving large probabilistic systems relies on aggregating states based on a measure of similarity. Many approaches in the literature are heuristic. A number of recent methods rely instead on metrics based on the notion of bisimulation, or behavioral equivalence between states (Givan et al, 2001, 2003; Ferns et al, 2004). An in...
Article
Full-text available
This paper proposes a definition of categorical model of the deep inference system BV, defined by Guglielmi. Deep inference introduces the idea of performing a deduction in the interior of a formula, at any depth. Traditional sequent calculus rules only see the roots of formulae. However in these new systems, one can rewrite at any position in the...
Conference Paper
Full-text available
We define an epistemic logic for labelled transition systems by introducing equivalence relations for the agents on the states of the labelled transition system. The idea is that agents observe the dynamics of the system modulo their ability to distinguish states and in the process learn about the current state and past history of the execution. Th...
Article
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The causal structure of spacetime defines a partial order on the events of spacetime. In an earlier paper, using techniques from domain theory, we showed that for globally hyperbolic spacetimes one could reconstruct the topology from the causal structure. However, the causal structure determines the metric only up to a local rescaling (a conformal...
Article
In the Fall of 1985 Dexter and I both started at Cornell as new faculty members in the celebrated Computer Science Department, home to luminaries such as Juris Hartmanis, John Hopcroft, David Gries and Robert Constable. I was a very new assistant professor but Dexter was already an acknowledged star with celebrated contributions to several areas: a...
Conference Paper
Full-text available
In this paper we consider the problem of representing and reasoning about systems, especially probabilistic systems, with hidden state. We consider transition systems where the state is not completely visible to an outside observer. Instead, there are observables that partly identify the state. We show that one can interchange the notions of state...
Conference Paper
Quantum field theory in curved spacetime reveals a fundamental ambiguity in the quantization procedure: the notion of vacuum, and hence of particles, is observer dependent. A state that an inertial observer in Minkowski space perceives to be the vacuum will appear to an accelerating observer to be a thermal bath of radiation. The impact of this Dav...
Conference Paper
I will present three main themes in current research in semantics: (a) models of programming languages, (b) concurrency and (c) approximation. The first theme covers denotational semantics and operational semantics and the search for tight connections between them. This led to the full abstraction problem and ultimately to game semantics. The secon...
Article
Full-text available
We reconsider discrete quantum causal dynamics where quantum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges depict propagation between events. Evolution is described as happening between a special family of spacelike slices, which were referred to as locative s...
Conference Paper
Full-text available
I give a non-comprehensive survey of the categorical quantum mechanics program and how it guides the search for structure in quantum computation. I discuss the example of measurement-based computing which is one of the successes of such an enterprise and briefly mention topological quantum computing which is an inviting target for future research i...
Chapter
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In nature one observes that in three space dimensions particles are either symmetric under interchange (bosons) or antisymmetric (fermions). These phases give rise to the two possible “statistics” that one observes. In two dimensions, however, a whole continuum of phases is possible. “Anyon” is a term coined in by Frank Wilczek to describe particle...
Chapter
Full-text available
The introduction of linear logic and its associated proof theory has revolutionized many semantical investigations, for example, the search for fully-abstract models of PCF and the analysis of optimal reduction strategies for lambda calculi. In the present paper we show how proof nets, a graph-theoretic syntax for linear logic proofs, can be interp...
Article
In recent years, various metrics have been developed for measuring the behavioral similarity of states in probabilistic transition systems [J. Desharnais et al., Proceedings of CONCUR'99, Springer-Verlag, London, 1999, pp. 258-273; F. van Breugel and J. Worrell, Proceedings of ICALP'01, Springer-Verlag, London, 2001, pp. 421-432]. In the context of...
Article
The decomposition based approximate numerical analysis of queueing networks of MAP/MAP/1 queues with FIFO scheduling is considered in this paper. One of the most crucial decisions of decomposition based queueing network analysis is the description of ...
Article
Full-text available
A state that an inertial observer in Minkowski space perceives to be the vacuum will appear to an accelerating observer to be a thermal bath of radiation. We study the impact of this Davies-Fulling-Unruh noise on communication, particularly quantum communication from an inertial sender to an accelerating observer and private communication between t...
Conference Paper
Full-text available
We develop an algebraic modal logic that combines epistemic and dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that “change the state” of the underlying system and not just the state of knowledge of the ag...
Article
DCM 2010 provides a forum for ideas about new computing means and models, with a particular emphasis in 2010 on computational and causal models related to physics and biology. We believe that bringing together different approaches - in a community with the strong foundational background characteristic of FLoC - results in inspirational cross-bounda...
Article
Full-text available
We develop an algebraic modal logic that combines epistemic modalities with dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that "change the state" of the underlying system and not just the state of knowledg...
Article
We investigate weak bisimulation of probabilistic systems in the presence of nondeterminism, i.e. labelled concurrent Markov chains (LCMC) with silent transitions. We build on the work of Philippou, Lee and Sokolsky [17] for finite state LCMCs. Their definition of weak bisimulation destroys the additivity property of the probability distributions,...
Conference Paper
Dynamic epistemic logic plays a key role in reasoning about multi-agent systems. Past approaches to dynamic epistemic logic have typically been focused on actions whose primary purpose is to communicate information from one agent to another. These actions are unable to alter the valuation of any proposition within the system. In fields such as secu...
Article
We investigate weak bisimulation of probabilistic systems in the presence of nondeterminism, i.e. labelled concurrent Markov chains (LCMC) with silent transitions. We develop an approach based on allowing convex combinations of computations, similar to Segala and Lynch’s use of randomized schedulers.The definition of weak bisimulation destroys the...
Article
Full-text available
Finding all the mutually unbiased bases in various dimensions is a problem of fundamental interest in quantum information theory and pure mathematics. The general problem formulated in finite-dimensional Hilbert spaces is open. In the categorical approach to quantum mechanics one can find examples of categories which behave ``like'' the category of...
Conference Paper
Full-text available
Labelled Markov processes are continuous-state fully probabilistic labelled transition systems. They can be seen as co-algebras of a suitable monad on the category of measurable space. The theory as developed so far included a treatment of bisimulation, logical characterization of bisimulation, weak bisimulation, metrics, universal domains for LMPs...
Conference Paper
We take a dual view of Markov processes – advocated by Kozen – as transformers of bounded measurable functions. We redevelop the theory of labelled Markov processes from this view point, in particular we explore approximation theory. We obtain three main results: (i) It is possible to define bisimulation on general measure spaces and show that it...
Book
Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and then develops the theory of LMPs. The main topics covered are bisimulation, the logical characterization of bisimulation, metrics and approximation theo...
Conference Paper
Full-text available
We explore equivalence relations between states in Markov Decision Processes and Partially Observ- able Markov Decision Processes. We focus on two different equivalence notions: bisimulation (Givan et al., 2003) and a notion of trace equivalence, un- der which states are considered equivalent if they generate the same conditional probability distri...
Conference Paper
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We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ul...
Article
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Randomized protocols for hiding private information can be regarded as noisy channels in the information-theoretic sense, and the inference of the concealed information can be regarded as a hypothesis-testing problem. We consider the Bayesian approach to the problem, and investigate the probability of error associated to the MAP (Maximum Aposterior...
Article
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We give a technique that can be used to prove that a given function is a measurement. We demonstrate its applicability by using it to resolve three notoriously difficult cases: capacity in information theory, entropy in quantum mechanics and global time in general relativity. We then show that this technique provides a new and surprising characteri...