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Abstract: The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use functi...
Abstract: We show that the problem of finding an optimal stochastic 'blind' controller in a Markov decision process is an NP-hard problem. The corresponding decision problem is NP-hard, in PSPACE, and...
Abstract: We extend a result by Lempp that recognising torsion-freeness for finitely presented groups is $\Pi^{0}_{2}$-complete; we show that the problem of recognising embeddings of finitely presente...
In this paper, we survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimizatio...
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed c...
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of compu...

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