Reverse mathematics and Weihrauch analysis motivated by finite complexity theory

BeMent, Zach; Hirst, Jeffry L.; Wallace, Asuka

doi:10.3233/com-210310

Cited by 2 publications

(1 citation statement)

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“…They address the question of whether there exist graphs for which determining their corresponding supergraph is more intricate. This question was initially posed in [13], where it was observed that for totally disconnected infinite graphs, deciding whether they are supergraphs of given graphs is equivalent to LPO, the simplest discontinuous problem. Cipriani and Pauly confirm the existence of a graph G such that LPO < W IS G while also exploring the complexity of the search problem.…”

Section: Supergraphsmentioning

confidence: 99%

Computable Analysis and Game Theory: From Foundations to Applications

Crook

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This body of research showcases several facets of the intersection between computer science and game theory. On the foundational side, we explore the obstructions to the computability of Nash equilibria in the setting of computable analysis. In particular, we study the Weihrauch degree of the problem of ﬁnding a Nash equilibrium for a multiplayer game in normal form. We conclude that the Weihrauch degree Nash for multiplayer games lies between AoUC∗[0,1] and AoUC⋄[0,1] (Theorem 5.3). As a slight detour, we also explore the demarcation between computable and non-computable computational problems pertaining to the veriﬁcation of machine learning. We demonstrate that many veriﬁcation questions are computable without the need to specify a machine learning framework (Section 7.2). As well as looking into the theory of learners, robustness and sparisty of training data. On the application side, we study the use of Hypergames in Cybersecurity. We look into cybersecurity AND/OR attack graphs and how we could turn them into a hypergame (8.1). Hyper Nash equilibria is not an ideal solution for these games, however, we propose a regret-minimisation based solution concept. In Section 8.2, we survey the area of Hypergames and their connection to cybersecurity, showing that even if there is a small overlap, the reach is limited. We suggest new research directions such as adaptive games, generalisation and transferability (Section 8.3).

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Section: Supergraphsmentioning

confidence: 99%