Maker-Maker and Maker-Breaker Games are PSPACE-Complete
TL;DR: The PSPACE-complete problem of deciding the outcome of Maker-Maker and Maker-Breaker games on arbitrary hypergraphs was shown to be PSPACEcomplete in this article.
Abstract: We show that the problems of deciding the outcome of Maker-Maker and Maker-Breaker games played on arbitrary hypergraphs are PSPACE-complete. Maker-Breaker games have earlier been shown PSPACE-complete by Schaefer (1978); we give a simpler proof and show a reduction from Maker-Maker games to Maker-Breaker games.
Citations
More filters
TL;DR: It is proved that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation, which provides a mathematical framework for extending domain theory and denotational semantics of programming languages to the more intricate models, languages and equivalences found in concurrent computation.
Abstract: This paper studies fundamental connections between profunctors (that is, distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Consequently, the composition of profunctors preserves open maps as 2-cells. A guiding idea is the view that profunctors, and colimit preserving functors, are linear maps in a model of classical linear logic. But profunctors, and colimit preserving functors, as linear maps, are too restrictive for many applications. This leads to a study of a range of pseudo-comonads and of how non-linear maps in their co-Kleisli bicategories preserve open maps and bisimulation. The pseudo-comonads considered are based on finite colimit completion, ‘lifting’, and indexed families. The paper includes an appendix summarising the key results on coends, left Kan extensions and the preservation of colimits. One motivation for this work is that it provides a mathematical framework for extending domain theory and denotational semantics of programming languages to the more intricate models, languages and equivalences found in concurrent computation, but the results are likely to have more general applicability because of the ubiquitous nature of profunctors.
74 citations
06 Jun 2005
TL;DR: The proof-carrying-request model is different than the notion of proof-of-compliance from traditional trust-management; in particular, all proofs are efficiently verifiable or easily rejected, but, in the worst case, may require as much communication as computing the actual trust-state itself.
Abstract: We consider distributed algorithms for solving a range of problems in a framework for trust in large-scale distributed systems. The framework is based on the notion of trust structures; a set of 'trust-levels' with two distinct partial orderings. In the trust model, a global trust-state is defined as the least fixed-point of a collection of local policies of nodes in the network. We show that it is possible to compute the global trust-state using a simple, robust and totally asynchronous distributed-algorithm. We also consider a distributed notion of proof-carrying-requests as a means of approximating the least fixed-point, enabling sound reasoning about the global trust-state without computing the exact fixed-point. Our proof-carrying-request model is different than the notion of proof-of-compliance from traditional trust-management; in particular, all proofs are efficiently verifiable or easily rejected, but, in the worst case, may require as much communication as computing the actual trust-state itself
33 citations
TL;DR: It is shown that reachability analysis for a replicative variant of the protocol becomes decidable, and the extended calculus is capable of an implicit description of the active intruder.
Abstract: We use some recent techniques from process algebra to draw several conclusions about the well studied class of ping-pong protocols introduced by Dolev and Yao. In particular we show that all nontrivial properties, including reachability and equivalence checking wrt. the whole van Glabbeek's spectrum, become undecidable for a very simple recursive extension of the protocol. The result holds even if no nondeterministic choice operator is allowed. We also show that the extended calculus is capable of an implicit description of the active intruder, including full analysis and synthesis of messages in the sense of Amadio, Lugiez and Vanackere. We conclude by showing that reachability analysis for a replicative variant of the protocol becomes decidable.
27 citations
26 Aug 2004
TL;DR: This work describes how to construct correct abstract machines from the class of L-attributed natural semantics and formalizes it as an extraction algorithm and proves that the algorithm produces abstract machines that are equivalent to the original natural semantics.
Abstract: We describe how to construct correct abstract machines from the class of L-attributed natural semantics introduced by Ibraheem and Schmidt at HOOTS 1997. The construction produces stack-based abstract machines where the stack contains evaluation contexts. It is defined directly on the natural semantics rules. We formalize it as an extraction algorithm and we prove that the algorithm produces abstract machines that are equivalent to the original natural semantics. We illustrate the algorithm by extracting abstract machines from natural semantics for call-by-value and call-by-name evaluation of lambda terms.
24 citations
TL;DR: It is shown that the set of fixed-point combinators forms a recursively-enumerable subset of a larger set of terms that is not Recursively enumerable, and the terms of which are observationally equivalent to fixed- point combinators in any computable context.
Abstract: We show that the set of fixed-point combinators forms a recursively-enumerable subset of a larger set of terms that is (A) not recursively enumerable, and (B) the terms of which are observationally equivalent to fixed-point combinators in any computable context.
17 citations
References
More filters
TL;DR: A number of two-person games, based on simple combinatorial ideas, for which the problem of deciding whether the first player can win is complete in polynomial space provides strong evidence, although not absolute proof, that efficient general algorithms for deciding the winner of these games do not exist.
311 citations
"Maker-Maker and Maker-Breaker Games..." refers background in this paper
...Maker-Breaker games have earlier been shown PSPACE-complete by Schaefer (1978); we give a simpler proof and show a reduction from Maker-Maker games to MakerBreaker games....
[...]
15 Aug 2004
TL;DR: The concept of zero-knowledge (ZK) has become of fundamental importance in cryptography as mentioned in this paper, and it has become one of the most important concepts in cryptography in the quantum setting.
Abstract: The concept of zero-knowledge (ZK) has become of fundamental importance in cryptography. However, in a setting where entities are modeled by quantum computers, classical arguments for proving ZK fail to hold since, in the quantum setting, the concept of rewinding is not generally applicable. Moreover, known classical techniques that avoid rewinding have various shortcomings in the quantum setting.
70 citations
TL;DR: This work shows Sigma^1_1-completeness of weak bisimilarity for PA (process algebra), and of weak simulation preorder/equivalence for PDA (pushdown automata), PA and PN (Petri nets).
Abstract: We show Sigma^1_1-completeness of weak bisimilarity for PA (process algebra), and of weak simulation preorder/equivalence for PDA (pushdown automata), PA and PN (Petri nets). We also show Pi^1_1-hardness of weak omega-trace equivalence for the (sub)classes BPA (basic process algebra) and BPP (basic parallel processes).
18 citations
TL;DR: A new notion of QZK, non-oblivious verifier QZk, is proposed, which is strictly stronger than honest-verifierQZK but weaker than full QK, and it is shown that this notion can be achieved by means of efficient (quantum) protocols.
Abstract: The concept of zero-knowledge (ZK) has become of fundamental importance in cryptography. However, in a setting where entities are modeled by quantum computers, classical arguments for proving ZK fail to hold since, in the quantum setting, the concept of rewinding is not generally applicable. Moreover, known classical techniques that avoid rewinding have various shortcomings in the quantum setting. We propose new techniques for building quantum zero-knowledge (QZK) protocols, which remain secure even under (active) quantum attacks. We obtain computational QZK proofs and perfect QZK arguments for any NP language in the common reference string model. This is based on a general method converting an important class of classical honest-verifier ZK (HVZK) proofs into QZK proofs. This leads to quite practical protocols if the underlying HVZK proof is efficient. These are the first proof protocols enjoying these properties, in particular the first to achieve perfect QZK. As part of our construction, we propose a general framework for building unconditionally hiding (trapdoor) string commitment schemes, secure against quantum attacks, as well as concrete instantiations based on specific (believed to be) hard problems. This is of independent interest, as these are the first unconditionally hiding string commitment schemes withstanding quantum attacks. Finally, we give a partial answer to the question whether QZK is possible in the plain model. We propose a new notion of QZK, non-oblivious verifier QZK, which is strictly stronger than honest-verifier QZK but weaker than full QZK, and we show that this notion can be achieved by means of efficient (quantum) protocols.
15 citations
04 Jul 2004
TL;DR: This work presents an efficient construction of a single polynomial of quite small degree whose zero set over Q;p; coincides with the zero setover Q; p; of the original system.
Abstract: For a system of polynomial equations over Q;p; we present an efficient construction of a single polynomial of quite small degree whose zero set over Q;p; coincides with the zero set over Q;p; of the original system. We also show that the polynomial has some other attractive features such as low additive and straight-line complexity.The proof is based on a link established here between the above problem and some recent number theoretic result about zeros of p-adic forms.
11 citations