Verifying pushdown multi-agent systems against strategy logics

In this paper, we investigate model checking algorithms for variants of strategy logic over pushdown multi-agent systems, modeled by pushdown game structures (PGSs). We consider various fragments of strategy logic, i.e., SL[CG], SL[DG], SL[1G] and BSIL. We show that the model checking problems on PGSs for SL[CG], SL[DG] and SL[1G] are 3EXTIME-complete, which are not harder than the problem for the subsumed logic ATL*. When BSIL is concerned, the model checking problem becomes 2EXPTIME-complete. Our algorithms are automata-theoretic and based on the saturation technique, which are amenable to implementations

On the satisfiability of indexed linear temporal logics

Indexed Linear Temporal Logics (ILTL) are an extension of standard Linear Temporal Logics (LTL) with quantifications over index variables which range over a set of process identifiers. ILTL has been widely used in specifying and verifying properties of parameterised systems, e.g., in parameterised model checking of concurrent processes. However there is still a lack of theoretical investigations on properties of ILTL, compared to the well-studied LTL. In this paper, we start to narrow this gap, focusing on the satisfiability problem, i.e., to decide whether a model exists for a given formula. This problem is in general undecidable. Various fragments of ILTL have been considered in the literature typically in parameterised model checking, e.g., ILTL formulae in prenex normal form, or containing only non-nested quantifiers, or admitting limited temporal operators. We carry out a thorough study on the decidability and complexity of the satisfiability problem for these fragments. Namely, for each fragment, we either show that it is undecidable, or otherwise provide tight complexity bounds

Investigations of the g factors and local structure for orthorhombic Cu^{2+}(1) site in fresh PrBa_{2}Cu_{3}O_{6+x} powders

The electron paramagnetic resonance (EPR) g factors g_x, g_y and g_z of the orthorhombic Cu^{2+}(1) site in fresh PrBa_{2}Cu_{3}O_{6+x} powders are theoretically investigated using the perturbation formulas of the g factors for a 3d^9 ion under orthorhombically elongated octahedra. The local orthorhombic distortion around the Cu^{2+}(1) site due to the Jahn-Teller effect is described by the orthorhombic field parameters from the superposition model. The [CuO6]^{10-} complex is found to experience an axial elongation of about 0.04 {\AA} along c axis and the relative bond length variation of about 0.09 {\AA} along a and b axes of the Jahn-Teller nature. The theoretical results of the g factors based on the above local structure are in reasonable agreement with the experimental data.Comment: 6 pages, 1 figur

Correlation between Voronoi volumes in disc packings

We measure the two-point correlation of free Voronoi volumes in binary disc packings, where the packing fraction $\phi_{\rm avg}$ ranges from 0.8175 to 0.8380. We observe short-ranged correlations over the whole range of $\phi_{\rm avg}$ and anti-correlations for $\phi_{\rm avg}>0.8277$. The spatial extent of the anti-correlation increases with $\phi_{\rm avg}$ while the position of the maximum of the anti-correlation and the extent of the positive correlation shrink with $\phi_{\rm avg}$. We conjecture that the onset of anti-correlation corresponds to dilatancy onset in this system

Thermodynamics of spin-1/2 tetrameric Heisenberg antiferromagnetic chain

The thermodynamic properties of a spin S=1/2 tetrameric Heisenberg antiferromagnetic chain with alternating interactions AF1-AF2-AF1-F (AF and F denote the antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the transfer-matrix renormalization group method and Jordan-Wigner transformation. It is found that in the absence of magnetic field, the thermodynamic behaviors are closely related to the gapped low-lying excitations, and a novel structure with three peaks in the temperature dependence of specific heat is unveiled. In a magnetic field, a phase diagram in the temperature-field plane for the couplings satisfying JAF1=JAF2=JF is obtained, in which various phases are identified. The temperature dependence of thermodynamic quantities including the magnetization, susceptibility and specific heat are studied to characterize the corresponding phases. It is disclosed that the magnetization has a crossover behavior at low temperature in the Luttinger liquid phase, which is shown falling into the same class as that in the S=1 Haldane chain. In the plateau regime, the thermodynamic behaviors alter at a certain field, which results from the crossing of two excitation spectra. By means of the fermion mapping, it is uncovered that the system has four spectra from fermion and hole excitations that are responsible for the observed thermodynamic behaviors.Comment: 10 pages, 10 figures, accepted by Phys. Rev.