New Pumping Technique for 2-Dimensional VASS

We propose a new pumping technique for 2-dimensional vector addition systems with states (2-VASS) building on natural geometric properties of runs. We illustrate its applicability by reproving an exponential bound on the length of the shortest accepting run, and by proving a new pumping lemma for languages of 2-VASS. The technique is expected to be useful for settling questions concerning languages of 2-VASS, e.g., for establishing decidability status of the regular separability problem

Reachability in Two-Dimensional Vector Addition Systems with States: One Test is for Free

Vector addition system with states is an ubiquitous model of computation with extensive applications in computer science. The reachability problem for vector addition systems is central since many other problems reduce to that question. The problem is decidable and it was recently proved that the dimension of the vector addition system is an important parameter of the complexity. In fixed dimensions larger than two, the complexity is not known (with huge complexity gaps). In dimension two, the reachability problem was shown to be PSPACE-complete by Blondin et al. in 2015. We consider an extension of this model, called 2-TVASS, where the first counter can be tested for zero. This model naturally extends the classical model of one counter automata (OCA). We show that reachability is still solvable in polynomial space for 2-TVASS. As in the work Blondin et al., our approach relies on the existence of small reachability certificates obtained by concatenating polynomially many cycles.Comment: Full version of the paper with the same title and authors in the proceedings of CONCUR 202

Reachability in Two-Dimensional Vector Addition Systems with States: One Test Is for Free

Vector addition system with states is an ubiquitous model of computation with extensive applications in computer science. The reachability problem for vector addition systems is central since many other problems reduce to that question. The problem is decidable and it was recently proved that the dimension of the vector addition system is an important parameter of the complexity. In fixed dimensions larger than two, the complexity is not known (with huge complexity gaps). In dimension two, the reachability problem was shown to be PSPACE-complete by Blondin et al. in 2015. We consider an extension of this model, called 2-TVASS, where the first counter can be tested for zero. This model naturally extends the classical model of one counter automata (OCA). We show that reachability is still solvable in polynomial space for 2-TVASS. As in the work Blondin et al., our approach relies on the existence of small reachability certificates obtained by concatenating polynomially many cycles

Asymptotic Complexity Estimates for Probabilistic Programs and Their VASS Abstractions

The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that this approach is not sufficiently robust, especially in situations when the expectations are infinite. We propose new estimates for the asymptotic analysis of probabilistic programs with non-deterministic choice that overcome this deficiency. Furthermore, we show how to efficiently compute/analyze these estimates for selected classes of programs represented as Markov decision processes over vector addition systems with states

Quantum coherent control of highly multipartite continuous-variable entangled states by tailoring parametric interactions

The generation of continuous-variable multipartite entangled states is important for several protocols of quantum information processing and communication, such as one-way quantum computation or controlled dense coding. In this article we theoretically show that multimode optical parametric oscillators can produce a great variety of such states by an appropriate control of the parametric interaction, what we accomplish by tailoring either the spatio-temporal shape of the pump, or the geometry of the nonlinear medium. Specific examples involving currently available optical parametric oscillators are given, hence showing that our ideas are within reach of present technology.Comment: 14 pages, 5 figure

Language Inclusion for Boundedly-Ambiguous Vector Addition Systems Is Decidable

We consider the problems of language inclusion and language equivalence for Vector Addition Systems with States (VASSes) with the acceptance condition defined by the set of accepting states (and more generally by some upward-closed conditions). In general the problem of language equivalence is undecidable even for one-dimensional VASSes, thus to get decidability we investigate restricted subclasses. On one hand we show that the problem of language inclusion of a VASS in k-ambiguous VASS (for any natural k) is decidable and even in Ackermann. On the other hand we prove that the language equivalence problem is Ackermann-hard already for deterministic VASSes. These two results imply Ackermann-completeness for language inclusion and equivalence in several possible restrictions. Some of our techniques can be also applied in much broader generality in infinite-state systems, namely for some subclass of well-structured transition systems

In situ study of oxidation states of platinum nanoparticles on a polymer electrolyte fuel cell electrode by near ambient pressure hard X-ray photoelectron spectroscopy

We performed in situ hard X-ray photoelectron spectroscopy (HAXPES) measurements of the electronic states of platinum nanoparticles on the cathode electrocatalyst of a polymer electrolyte fuel cell (PEFC) using a near ambient pressure (NAP) HAXPES instrument having an 8 keV excitation source. We successfully observed in situ NAP-HAXPES spectra of the Pt/C cathode catalysts of PEFCs under working conditions involving water, not only for the Pt 3d states with large photoionization cross-sections in the hard X-ray regime but also for the Pt 4f states and the valence band with small photoionization cross-sections. Thus, this setup allowed in situ observation of a variety of hard PEFC systems under operating conditions. The Pt 4f spectra of the Pt/C electrocatalysts in PEFCs clearly showed peaks originating from oxidized Pt(II) at 1.4 V, which unambiguously shows that Pt(IV) species do not exist on the Pt nanoparticles even at such large positive voltages. The water oxidation reaction might take place at that potential (the standard potential of 1.23 V versus a standard hydrogen electrode) but such a reaction should not lead to a buildup of detectable Pt(IV) species. The voltage-dependent NAP-HAXPES Pt 3d spectra revealed different behaviors with increasing voltage (0.6 → 1.0 V) compared with decreasing voltage (1.0 → 0.6 V), showing a clear hysteresis. Moreover, quantitative peak-fitting analysis showed that the fraction of non-metallic Pt species matched the ratio of the surface to total Pt atoms in the nanoparticles, which suggests that Pt oxidation only takes place at the surface of the Pt nanoparticles on the PEFC cathode, and the inner Pt atoms do not participate in the reaction. In the valence band spectra, the density of electronic states near the Fermi edge reduces with decreasing particle size, indicating an increase in the electrocatalytic activity. Additionally, a change in the valence band structure due to the oxidation of platinum atoms was also observed at large positive voltages. The developed apparatus is a valuable in situ tool for the investigation of the electronic states of PEFC electrocatalysts under working conditions