Reachability in Cooperating Systems with Architectural Constraints is PSPACE-Complete

The reachability problem in cooperating systems is known to be PSPACE-complete. We show here that this problem remains PSPACE-complete when we restrict the communication structure between the subsystems in various ways. For this purpose we introduce two basic and incomparable subclasses of cooperating systems that occur often in practice and provide respective reductions. The subclasses we consider consist of cooperating systems the communication structure of which forms a line respectively a star.Comment: In Proceedings GRAPHITE 2013, arXiv:1312.706

Complexity Results for Modal Dependence Logic

Modal dependence logic was introduced recently by V\"a\"an\"anen. It enhances the basic modal language by an operator =(). For propositional variables p_1,...,p_n, =(p_1,...,p_(n-1);p_n) intuitively states that the value of p_n is determined by those of p_1,...,p_(n-1). Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time. In this paper we consider fragments of modal dependence logic obtained by restricting the set of allowed propositional connectives. We show that satisfibility for poor man's dependence logic, the language consisting of formulas built from literals and dependence atoms using conjunction, necessity and possibility (i.e., disallowing disjunction), remains NEXPTIME-complete. If we only allow monotone formulas (without negation, but with disjunction), the complexity drops to PSPACE-completeness. We also extend V\"a\"an\"anen's language by allowing classical disjunction besides dependence disjunction and show that the satisfiability problem remains NEXPTIME-complete. If we then disallow both negation and dependence disjunction, satistiability is complete for the second level of the polynomial hierarchy. In this way we completely classify the computational complexity of the satisfiability problem for all restrictions of propositional and dependence operators considered by V\"a\"an\"anen and Sevenster.Comment: 22 pages, full version of CSL 2010 pape

On Negotiation as Concurrency Primitive

We introduce negotiations, a model of concurrency close to Petri nets, with multiparty negotiation as primitive. We study the problems of soundness of negotiations and of, given a negotiation with possibly many steps, computing a summary, i.e., an equivalent one-step negotiation. We provide a complete set of reduction rules for sound, acyclic, weakly deterministic negotiations and show that, for deterministic negotiations, the rules compute the summary in polynomial time

Increasing the power of the verifier in Quantum Zero Knowledge

In quantum zero knowledge, the assumption was made that the verifier is only using unitary operations. Under this assumption, many nice properties have been shown about quantum zero knowledge, including the fact that Honest-Verifier Quantum Statistical Zero Knowledge (HVQSZK) is equal to Cheating-Verifier Quantum Statistical Zero Knowledge (QSZK) (see [Wat02,Wat06]). In this paper, we study what happens when we allow an honest verifier to flip some coins in addition to using unitary operations. Flipping a coin is a non-unitary operation but doesn't seem at first to enhance the cheating possibilities of the verifier since a classical honest verifier can flip coins. In this setting, we show an unexpected result: any classical Interactive Proof has an Honest-Verifier Quantum Statistical Zero Knowledge proof with coins. Note that in the classical case, honest verifier SZK is no more powerful than SZK and hence it is not believed to contain even NP. On the other hand, in the case of cheating verifiers, we show that Quantum Statistical Zero Knowledge where the verifier applies any non-unitary operation is equal to Quantum Zero-Knowledge where the verifier uses only unitaries. One can think of our results in two complementary ways. If we would like to use the honest verifier model as a means to study the general model by taking advantage of their equivalence, then it is imperative to use the unitary definition without coins, since with the general one this equivalence is most probably not true. On the other hand, if we would like to use quantum zero knowledge protocols in a cryptographic scenario where the honest-but-curious model is sufficient, then adding the unitary constraint severely decreases the power of quantum zero knowledge protocols.Comment: 17 pages, 0 figures, to appear in FSTTCS'0

Quantum Proofs

Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in which a quantum state plays the role of a proof (also called a certificate or witness), and is checked by a polynomial-time quantum computation. For some problems, the fact that a quantum proof state could be a superposition over exponentially many classical states appears to offer computational advantages over classical proof strings. In the interactive proof system setting, one may consider a verifier and one or more provers that exchange and process quantum information rather than classical information during an interaction for a given input string, giving rise to quantum complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit some properties from their classical counterparts, they also possess distinct and uniquely quantum features that lead to an interesting landscape of complexity classes based on variants of this model. In this survey we provide an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, we discuss non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class \class{QSZK}, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*.Comment: Survey published by NOW publisher

Verification of Information Flow Properties under Rational Observation

Information flow properties express the capability for an agent to infer information about secret behaviours of a partially observable system. In a language-theoretic setting, where the system behaviour is described by a language, we define the class of rational information flow properties (RIFP), where observers are modeled by finite transducers, acting on languages in a given family $\mathcal{L}$. This leads to a general decidability criterion for the verification problem of RIFPs on $\mathcal{L}$, implying PSPACE-completeness for this problem on regular languages. We show that most trace-based information flow properties studied up to now are RIFPs, including those related to selective declassification and conditional anonymity. As a consequence, we retrieve several existing decidability results that were obtained by ad-hoc proofs.Comment: 19 pages, 7 figures, version extended from AVOCS'201

Equivalence-Checking on Infinite-State Systems: Techniques and Results

The paper presents a selection of recently developed and/or used techniques for equivalence-checking on infinite-state systems, and an up-to-date overview of existing results (as of September 2004)

Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete

Ergodic quantum computing

We propose a (theoretical ;-) model for quantum computation where the result can be read out from the time average of the Hamiltonian dynamics of a 2-dimensional crystal on a cylinder. The Hamiltonian is a spatially local interaction among Wigner-Seitz cells containing 6 qubits. The quantum circuit that is simulated is specified by the initialization of program qubits. As in Margolus' Hamiltonian cellular automaton (implementing classical circuits), a propagating wave in a clock register controls asynchronously the application of the gates. However, in our approach all required initializations are basis states. After a while the synchronizing wave is essentially spread around the whole crystal. The circuit is designed such that the result is available with probability about 1/4 despite of the completely undefined computation step. This model reduces quantum computing to preparing basis states for some qubits, waiting, and measuring in the computational basis. Even though it may be unlikely to find our specific Hamiltonian in real solids, it is possible that also more natural interactions allow ergodic quantum computing.Comment: latex, 25 pages, 10 figures (colored