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An $\mathsf{F}_{d}$ upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where $\mathsf{F}_d$ is the $d$-th level of the Grzegorczyk hierarchy of complexity classes. The new algorithm combines the idea of the linear path scheme characterization of the reachability in the $2$-dimension VASSes with the general decomposition algorithm by Mayr, Kosaraju and Lambert. The result improves the $\mathsf{F}_{d + 4}$ upper bound due to Leroux and Schmitz (LICS 2019)., Comment: 36 pages

Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several divergence-sensitive refinements of branching and weak probabilistic bisimilarities have been proposed in the literature. Both the definitions of these equivalences and the techniques to investigate them differ significantly. This paper presents a comprehensive comparative study on divergence-sensitive behavioral equivalence relations that refine the branching and weak probabilistic bisimilarities. Additionally, these equivalence relations are shown to have efficient checking algorithms. The techniques of this paper might be of independent interest in a more general setting.

The reachability problem for vector addition systems with states (VASS) has been shown to be \textsc{Ackermann}-complete. For every $k\geq 3$, a completeness result for the $k$-dimensional VASS reachability problem is not yet available. It is shown in this paper that the $3$-dimensional VASS reachability problem is in \textsc{Tower}, improving upon the current best upper bound $\mathbf{F}_7$ established by Leroux and Schmidt in 2019., Comment: 23 pages, 1 figure

We present a novel approach named as pumping ionizing gating (PIG) for the generation of isolated attosecond pulses (IAPs). In this regime, a short laser is used to ionize a pre-existing gas grating, creating a fast-extending plasma grating(FEPG) having an ionization front propagating with the velocity of light. A low-intensity long counterpropagating pump pulse is then reflected by a very narrow region of the ionization front, only where the Bragg conditions for resonant reflection is satisfied. Consequently, the pump reflection is confined within a sub-cycle region called PIG, and forms a wide-band coherent IAP in combination with the frequency up-conversion effect due to the plasma gradient. This approach results in a new scheme to generate IAPs fromlong picosecond pump pulses. Three-dimensional (3D) simulations show that a 1.6-ps, 1-{\mu}m pump pulse can be used to generate a 330 as laser pulse with a peak intensity approximately 33 times that of the pump and a conversion efficiency of around 0.1%.These results highlight the potential of the PIG method for generating IAPs with high conversion efficiency and peak intensity., Comment: It provides a new way to generate isolated attosecond pulse(IAP) by a picosecond pump, which has a protential to boost the IAP energy to joule level

The bottleneck for an attosecond science experiment is concluded to be the lack of a high-peak-power isolated attosecond pulse source. Therefore, currently, generating an intense attosecond pulse would be one of the highest priority goals. In this paper, we review a TW-class parallel three-channel waveform synthesizer for generating a gigawatt-scale soft-x-ray isolated attosecond pulse (IAP) using high-order harmonics generation (HHG). Simultaneously, using several stabilization methods, namely, the low-repetition-rate laser carrier-envelope phase stabilization, Mach-Zehnder interferometer, balanced optical cross-correlator, and beam-pointing stabilizer, we demonstrate a stable 50-mJ three-channel optical-waveform synthesizer with a peak power at the multi-TW level. This optical-waveform synthesizer is capable of creating a stable intense optical field for generating an intense continuum harmonic beam thanks to the successful stabilization of all the parameters. Furthermore, the precision control of shot-to-shot reproducible synthesized waveforms is achieved. Through the HHG process employing a loose-focusing geometry, an intense shot-to-shot stable supercontinuum (50-70 eV) is generated in an argon gas cell. This continuum spectrum supports an IAP with a transform-limited duration of 170 as and a submicrojoule pulse energy, which allows the generation of a GW-scale IAP. Another supercontinuum in the soft-x-ray region with higher photon energy of approximately 100-130 eV is also generated in neon gas from the synthesizer. The transform-limited pulse duration is 106 as. According to this work, the enhancement of HHG output through optimized waveform synthesis is experimentally proved. The high-energy multicycle pulse with 10-Hz repetition rate is proved to have the same controllability for optimized waveform synthesis for HHG as few- or subcycle pulses from a 1-kHz laser., Comment: 21 pages, 10 figures

We demonstrate an efficient procedure for terahertz-wave radiation generation by applying a nonlinear wavelength conversion approach using a mid-infrared pump source. We used a 3.3 {\mu}m dual-chirped optical parametric amplification source and a 1.5 {\mu}m fiber laser for a comparison of energy conversion efficiencies. Nonlinear inorganic and organic crystals were used, and for the periodically-poled lithium niobate crystal, the efficiencies were 1.3*10^-4 and 5.6*10^-12 for the 3.3 {\mu}m source and the 1.5 {\mu}m source, respectively. We confirmed that nonlinear crystals could be pumped with tera-watt / cm^2 class by using an mid-infrared source, which reduces several undesirable nonlinear optical effects., Comment: 7 pages, 4figures

In our recent study [Commun. Phys. 3, 92 (2020)], we have developed an approach for energy-scaling of high-order harmonic generation in water-window region under neutral-medium condition. More specifically, we obtained nanojoule-class water-window soft x-ray harmonic beam under phase match condition. It has been achieved by combining a newly developed terawatt-class mid-infrared femtosecond laser and a loose focusing geometry for high-order harmonic generation. The generated beam is more than 100 times intense compared to previously reported results. The experimental setup included two key parts: terawatt mid-infrared femtosecond driving laser [ Sci. Rep. 8, 7692 (2018)] and specially designed gas cell. Despite the dramatic drop in the optimal gas pressure due to loose focusing geometry, it still reached 1 bar level for helium. Moreover, faster leaking speed caused by larger pinhole size of the gas cell made the use of a normal gas cell impossible. Thus, we have designed a double-structured pulsed-gas cell with a differential pumping system, which enabled providing sufficiently high gas pressure. Moreover, it allowed reducing gas consumption significantly. Robust energy-scalable apparatus for high-order harmonic generation developed in in this study will enable the generation of over tens nanojoule water-window attosecond pulses in the nearest future., Comment: 10 pages, 8 figures

Full coherent soft X-ray attosecond pulses are now available through high-order harmonic generation (HHG); however, its insufficient output energy hinders various applications, such as attosecond-scale soft X-ray nonlinear experiments, the seeding of soft X-ray free-electron lasers, attosecond-pump-attosecond-probe spectroscopies, and single-shot imaging. In this paper, towards the implementation of these exciting studies, we demonstrate a soft X-ray harmonic beam that is more than two orders of magnitudes stronger up to the water window region compared to previous works. This was achieved by combining a newly developed TW class mid-infrared femtosecond laser and a loosely focusing geometry for HHG in the mid-infrared region for the first time. Thanks to a loosely focusing geometry with a neutral medium target, we achieve a high conversion efficiency, a low beam divergence, and a significantly reduced medium gas pressure. As the first application of our nano-joule level water window soft X-ray harmonic source, we demonstrate near edge X-ray absorption fine structure (NEXAFS) experiments with clear fine absorption spectra near the K- and L-edges observed in various samples. The systematic study of a robust energy scaling method on HHG opens the door for demonstrating single-shot absorption spectrum and live cell imaging with a femtosecond time resolution., Comment: 9 pages, 7 figures

A complete characterization of the complexity of the reachability problem for vector addition system has been open for a long time. The problem is shown to be Tower complete., Comment: We apply to with draw this paper because there is a fatal error. At the moment we do not know how correct the mistake

A stable 50 mJ three-channel optical waveform synthesizer is demonstrated and used to reproducibly generate a high-order harmonics supercontinuum in the soft-x-ray region. This synthesizer is composed of pump pulses from a 10-Hz-repetition-rate Ti:sapphire pump laser and signal and idler pulses from an infrared two-stage optical parametric amplifier driven by this pump laser. With the full active stabilization of all relative time delays, relative phases, and the carrier-envelope phase, a shot-to-shot stable intense continuum harmonic spectrum is obtained around 60 eV with pulse energy above 0.24 $\mu$J. The peak power of the soft-x-ray continuum is evaluated to be beyond 1 GW with a 140 as transform limit duration. Furthermore, we found a characteristic delay dependence of the multi-cycle waveform synthesizer and established its control scheme. Compared with the one-color case, we experimentally observe an enhancement of the cut-off spectrum intensity by one to two orders of magnitude through the three-color waveform synthesis., Comment: 19 pages, 6 figures, this is the submitted version of the paper that has been accepted to Science Advances. The final and revised version will be available after publication in the journal

This paper presents the optimization of a dual-chirped optical parametric amplification (DC-OPA) scheme for producing an ultrafast intense infrared (IR) pulse. By employing a total energy of 0.77 J Ti:sapphire pump laser and type-I BBO crystals, an IR pulse energy at the center wavelength of 1.7 $\mu$m exceeded 0.1 J using the optimized DC-OPA. By adjusting the injected seed spectrum and prism pair compressor with a gross throughput of over 70 \%, the 1.7-$\mu$m pulse was compressed to 31 fs, which resulted in a peak power of up to 2.3 TW. Based on the demonstration of the BBO type-I DC-OPA, we propose a novel OPA scheme called the $dual~pump$ DC-OPA for producing a high-energy IR pulse with a two-cycle duration., Comment: 9 pages, 7 figures

There is a lot of research on probabilistic transition systems. There are not many studies in probabilistic process models. The lack of investigation into the interactive aspect of probabilistic processes is mainly due to the difficulty caused by the discrepancy between probabilistic actions and nondeterministic behaviours. The paper proposes a uniform approach to probabilistic process models and a bisimulation congruence for probabilistic concurrency.

A universal process of a process calculus is one that, given the G\"{o}del index of a process of a certain type, produces a process equivalent to the encoded process. This paper demonstrates how universal processes can be formally defined and how a universal process of the value-passing calculus can be constructed. The existence of such a universal process in a process model can be explored to implement higher order communications, security protocols, and programming languages in the process model. A process version of the S-m-n theorem is stated to showcase how to embed the recursion theory in a process calculus.

Name-passing calculi are foundational models for mobile computing. Research into these models has produced a wealth of results ranging from relative expressiveness to programming pragmatics. The diversity of these results call for clarification and reorganization. This paper applies a model independent approach to the study of the name-passing calculi, leading to a uniform treatment and simplification. The technical tools and the results presented in the paper form the foundation for a theory of name-passing calculus.

Senizergues has proved that language equivalence is decidable for disjoint epsilon-deterministic PDA. Stirling has showed that strong bisimilarity is decidable for PDA. On the negative side Srba demonstrated that the weak bisimilarity is undecidable for normed PDA. Later Jancar and Srba established the undecidability of the weak bisimilarity for disjoint epsilon-pushing PDA and disjoint epsilon-popping PDA. These decidability and undecidability results are extended in the present paper. The extension is accomplished by looking at the equivalence checking issue for the branching bisimilarity of several variants of PDA., Comment: 26 pages, 9 figures

Recent studies reveal that branching bisimilarity is decidable for both nBPP (normed Basic Parallel Process) and nBPA (normed Basic Process Algebra). These results lead to the question if there are any other models in the hierarchy of PRS (Process Rewrite System) whose branching bisimilarity is decidable. It is shown in this paper that the branching bisimilarity for both nOCN (normed One Counter Net) and nPA (normed Process Algebra) is undecidable. These results essentially imply that the question has a negative answer., Comment: 18 pages, 6 Figures