Observation and Distinction. Representing Information in Infinite Games

We compare two approaches for modelling imperfect information in infinite games by using finite-state automata. The first, more standard approach views information as the result of an observation process driven by a sequential Mealy machine. In contrast, the second approach features indistinguishability relations described by synchronous two-tape automata. The indistinguishability-relation model turns out to be strictly more expressive than the one based on observations. We present a characterisation of the indistinguishability relations that admit a representation as a finite-state observation function. We show that the characterisation is decidable, and give a procedure to construct a corresponding Mealy machine whenever one exists

Bleeding Words: Louise Bourgeois' and José Leonilson's Love Images

As one tries to grasp love and its images within José Leonilson's production, a multiplicity of aspects and meanings are seen that also relate to Louise Bourgeois's oeuvre in regard to the interest in human relations. Through a comparative approach to both artists' poetics, an understanding is created that love is not a simplistic action and all the words read in or applied to their visual discourse must be considered within a wide range of love in visual and literary images. Keywords: literature and visual arts / love / creativity / Bourgeois, Louise / Leonilson, José / word and image

Infinite games with finite knowledge gaps

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow. Instead, our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play. We show that it is decidable whether a given game satisfies the condition, and prove tight complexity bounds for the strategy synthesis problem under $\omega$-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio

Games with recurring certainty

Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players become uncertain about the current state of the game, and this uncertainty lasts forever. Here we consider games where the players attain certainty about the current state over and over again along any play. For finite-state games, we note that this kind of recurring certainty implies a stronger condition of periodic certainty, that is, the events of state certainty ultimately occur at uniform, regular intervals. We show that it is decidable whether a given game presents recurring certainty, and that, if so, the problem of synthesising coordination strategies under w-regular winning conditions is solvable.Comment: In Proceedings SR 2014, arXiv:1404.041

Undirected Graphs of Entanglement Two

Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at most k. As this measure is defined by means of games, game theoretic ideas naturally lead to design polynomial algorithms that, for fixed k, decide the problem. Known characterizations of directed graphs of entanglement at most 1 lead, for k = 1, to design even faster algorithms. In this paper we present an explicit characterization of undirected graphs of entanglement at most 2. With such a characterization at hand, we devise a linear time algorithm to decide whether an undirected graph has this property

Games with Delays. A Frankenstein Approach

We investigate infinite games on finite graphs where the information flow is perturbed by nondeterministic signalling delays. It is known that such perturbations make synthesis problems virtually unsolvable, in the general case. On the classical model where signals are attached to states, tractable cases are rare and difficult to identify. Here, we propose a model where signals are detached from control states, and we identify a subclass on which equilibrium outcomes can be preserved, even if signals are delivered with a delay that is finitely bounded. To offset the perturbation, our solution procedure combines responses from a collection of virtual plays following an equilibrium strategy in the instant- signalling game to synthesise, in a Frankenstein manner, an equivalent equilibrium strategy for the delayed-signalling game

The British Foreign Service and the American Civil War

During the American Civil War, the British legation and consuls experienced strained relations with both the Union and the Confederacy, to varying degrees and with different results. Southern consuls were cut off from the legation in Washington, D.C., and confronted their problems for the most part without direction from superiors. Consuls in the North sought assistance from the British foreign minister and followed the procedures he established. Diplomatic relations with Great Britain eased tensions in the North; the British consuls in the South were expelled in 1863. Eugene H. Berwanger uses archival sources in both Britain and the United States as a basis for his reevaluation of consular attitudes. Because much of this material was not available to earlier historians of British-American diplomacy, the author expands upon their conclusions and suggests reinterpretations in light of the new information. The first comprehensive investigation of Anglo-American relations during the Civil War, The British Foreign Service and the American Civil War will interest scholars of American history and diplomatic relations. Eugene Berwanger is professor of history at Colorado State University and author of several other books on American history.https://uknowledge.uky.edu/upk_diplomatic_history/1000/thumbnail.jp