297 research outputs found
A Coalgebraic View on Reachability
Coalgebras for an endofunctor provide a category-theoretic framework for
modeling a wide range of state-based systems of various types. We provide an
iterative construction of the reachable part of a given pointed coalgebra that
is inspired by and resembles the standard breadth-first search procedure to
compute the reachable part of a graph. We also study coalgebras in Kleisli
categories: for a functor extending a functor on the base category, we show
that the reachable part of a given pointed coalgebra can be computed in that
base category
Fixed Points Theorems for Non-Transitive Relations
In this paper, we develop an Isabelle/HOL library of order-theoretic
fixed-point theorems. We keep our formalization as general as possible: we
reprove several well-known results about complete orders, often with only
antisymmetry or attractivity, a mild condition implied by either antisymmetry
or transitivity. In particular, we generalize various theorems ensuring the
existence of a quasi-fixed point of monotone maps over complete relations, and
show that the set of (quasi-)fixed points is itself complete. This result
generalizes and strengthens theorems of Knaster-Tarski, Bourbaki-Witt, Kleene,
Markowsky, Pataraia, Mashburn, Bhatta-George, and Stouti-Maaden
Negotiation protocols and dynamic social networks
International audienceMulti-agent system make it possible to investigate systems with complex interaction protocols and limited information sharing. Our objective in this paper is to emphasize the impact of exchange protocols in social networks. The presented MAS considers a loan-granting scenario where each agent can borrow/lend money to its neighbors and/or consume it. We define six interaction protocols, ranging from fixed equilibrium rate loans to double-free auctions, and we study their impact on the network structure and the global welfare of the economy. Further, the agent fitness is investigated in relation with its connectivity (number of neighbors) and eccentricity (longest path to the other agents)
Economy-driven Shaping of Social Networks and Emerging Class Behaviors
International audienceIn this paper, we propose an agent-based analysis of a cumulative social-network game. Agents grant loans to their neighbours to maximize their intertemporal utility function. With a complete graph, we show that interest rates converge toward the theoretical equilibrium, even if ther is no centralized walrasian auctioneer and no preference transmition between agents. With a dynamic network, we explain why the network can't stabilize with a rational strategy. We introduce death and show that, even if the rational strategy is individually the best, the situation where three different strategies coexist is better for the global welfare
A Categorical Framework for Program Semantics and Semantic Abstraction
Categorical semantics of type theories are often characterized as
structure-preserving functors. This is because in category theory both the
syntax and the domain of interpretation are uniformly treated as structured
categories, so that we can express interpretations as structure-preserving
functors between them. This mathematical characterization of semantics makes it
convenient to manipulate and to reason about relationships between
interpretations. Motivated by this success of functorial semantics, we address
the question of finding a functorial analogue in abstract interpretation, a
general framework for comparing semantics, so that we can bring similar
benefits of functorial semantics to semantic abstractions used in abstract
interpretation. Major differences concern the notion of interpretation that is
being considered. Indeed, conventional semantics are value-based whereas
abstract interpretation typically deals with more complex properties. In this
paper, we propose a functorial approach to abstract interpretation and study
associated fundamental concepts therein. In our approach, interpretations are
expressed as oplax functors in the category of posets, and abstraction
relations between interpretations are expressed as lax natural transformations
representing concretizations. We present examples of these formal concepts from
monadic semantics of programming languages and discuss soundness.Comment: MFPS 202
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