Rm NP Research Articles

The Computational Complexity of Feasibility Analysis for Conditional DAG Tasks

The Conditional DAG (CDAG) task model is used for modeling multiprocessor real-time systems containing conditional expressions for which outcomes are not known prior to their evaluation. Feasibility analysis for CDAG tasks upon multiprocessor platforms is shown to be complete for the complexity class pspace ; assuming np ≠ pspace , this result rules out the use of Integer Linear Programming solvers for solving this problem efficiently. It is further shown that there can be no pseudo-polynomial time algorithm that solves this problem unless p = pspace .

Models of Bounded Arithmetic Theories and Some Related Complexity Questions

In this paper, we study bounded versions of some model-theoretic notions and results. We apply these results to the context of models of bounded arithmetic theories as well as some related complexity questions. As an example, we show that if the theory \(\rm S_2 ^1(PV)\) has bounded model companion then \(\rm NP=coNP\). We also study bounded versions of some other related notions such as Stone topology.

A unique discrimination between new physics scenarios in $$b\rightarrow s\mu ^+\mu ^-$$ anomalies

A number of observables related to the $b \to s \ell^+ \ell^-$ transition show deviations from their standard model predictions. A global fit to the current $b\rightarrow s\ell^+\ell^-$ data suggests several new physics solutions. Considering only one operator at a time and new physics only in the muon sector, it has been shown that the new physics scenarios (I) $C_9^{\rm NP}<0$, (II) $C_{9}^{\rm NP} = -C_{10}^{\rm NP}$, (III) $C_9^{\rm NP} = -C_9^{\prime \rm NP}$ can account for all data. In this work, we develop a procedure to uniquely identify the correct new physics solution. The scenario II predicts a significantly lower value of $\mathcal{B}(B_s\to \mu^+\mu^-)$ and can be distinguished from the other two scenarios if the experimental uncertainty comes down by a factor of three. On the other hand, a precise measurement of the CP averaged angular observables $S_9$ in high $q^2$ bin of $B\to K^*\mu^+\mu^-$ decay can uniquely discriminate between the other two scenarios. We propose new methods, in terms of azimuthal angle asymmetries, to measure $S_9$ with the necessary precision.

Measuring neutron skin by grazing isobaric collisions

Neutron skin thickness ($\Delta r_{\rm np}$) of nuclei and the inferred nuclear symmetry energy are of critical importance to nuclear physics and astrophysics. It is traditionally measured by nuclear processes with significant theoretical uncertainties. We recently proposed an indirect measurement of the $\Delta r_{\rm np}$ by charged hadron multiplicities in central isobaric collisions at relativistic energies, which are sensitive to nuclear densities. In this Letter, we propose a direct measurement of the $\Delta r_{\rm np}$ by using net-charge multiplicities in ultra-peripheral (grazing) collisions of those isobars, under the assumption that they are simple superimposition of nucleon-nucleon interactions. We illustrate this novel approach by the TRENTO and URQMD models.

Studying the b→sℓ+ℓ− anomalies and (g−2)μ in R -parity violating MSSM framework with the inverse seesaw mechanism

Inspired by the recent experimental results which show deviations from the standard model (SM) predictions of $b\rightarrow s \ell^+\ell^-$ transitions, we study the $R$-parity violating minimal supersymmetric standard model (RPV-MSSM) extended by the inverse seesaw mechanism. The trilinear $R$-parity violating terms, together with the chiral mixing of sneutrinos, induce the loop contributions to the $b\rightarrow s \ell^+\ell^-$ anomaly. We study the parameter space of the single-parameter scenario $C^{\rm NP}_{9,\mu}=-C^{\rm NP}_{10,\mu}=C_{\rm V}$ and the double-parameter scenario $(C_{\rm V},C_{\rm U})$, respectively, constrained by other experimental data such as $B_s-\bar{B}_s$ mixing, $B\rightarrow X_s \gamma$ decay, the lepton flavour violating decays, etc. Both the single-parameter and the double-parameter scenario can resolve the long existing muon anomalous magnetic moment problem as well, and allow the anomalous $t\rightarrow cg$ process to reach the sensitivity at the Future Circular hadron-hadron Collider (FCC-hh).

Implication of K→πνν¯ for generic neutrino interactions in effective field theories

In this work we investigate the implication of $K\to \pi \nu \bar{\nu}$ from the recent KOTO and NA62 measurements for generic neutrino interactions and the new physics scale in effective field theories. The interactions between quarks and left-handed Standard Model (SM) neutrinos are first described by the low energy effective field theory (LEFT) below the electroweak scale. We match them to the chiral perturbation theory ($\chi$PT) at the chiral symmetry breaking scale to calculate the branching fractions of Kaon semi-invisible decays and match them up to the SM effective field theory (SMEFT) to constrain new physics above the electroweak scale. In the framework of effective field theories, we prove that the Grossman-Nir bound is valid for both dim-6 and dim-7 LEFT operators, and the dim-6 vector and scalar operators dominantly contribute to Kaon semi-invisible decays based on LEFT and chiral power counting rules. They are induced by multiple dim-6 lepton-number-conserving operators and one dim-7 lepton-number-violating operator in the SMEFT, respectively. In the lepton-number-conserving $s\to d$ transition, the $K\to \pi \nu \bar{\nu}$ decays provide the most sensitive probe for the operators with $\tau\tau$ component and point to a corresponding new physics scale of $\Lambda_{\rm NP} \in[47~\text{TeV},~72~\text{TeV}]$ associated with a single effective coefficient. The lepton-number-violating operator can also explain the observed $K\to\pi\nu\bar{\nu}$ discrepancy with the SM prediction within a narrow range $\Lambda_{\rm NP}\in [19.4~\text{TeV},~21.5~\text{TeV}]$, which is consistent with constraints from Kaon invisible decays.

Interactive proofs and a Shamir-like result for real number computations

We introduce and study interactive proofs in the framework of real number computations as introduced by Blum, Shub, and Smale. Ivanov and de Rougemont started this line of research showing that an analogue of Shamir’s result holds in the real additive Blum–Shub–Smale model of computation when only Boolean messages can be exchanged. Here, we introduce interactive proofs in the full BSS model in which also multiplications can be performed and reals can be exchanged. The ultimate goal is to give a Shamir-like characterization of the real counterpart $${{\rm IP}_\mathbb{R}}$$ of classical IP. Whereas classically Shamir’s result implies IP = PSPACE = PAT = PAR, in our framework a major difficulty arises: In contrast to Turing complexity theory, the real number classes $${{\rm PAR}_\mathbb{R}}$$ and $${{\rm PAT}_\mathbb{R}}$$ differ and space resources considered separately are not meaningful. It is not obvious how to figure out whether at all $${{\rm IP}_\mathbb{R}}$$ is characterized by one of the above classes—and if so by which. We obtain two main results, an upper and a lower bound for the new class $${{\rm IP}_\mathbb{R}.}$$ As upper bound we establish $${{{\rm IP}_\mathbb{R}} \subseteq {\rm MA\exists}_\mathbb{R}}$$ , where $${{\rm MA} \exists_\mathbb{R}}$$ is a real complexity class introduced by Cucker and Briquel satisfying $${{\rm PAR}_\mathbb{R} \subsetneq {\rm MA}\exists_{\mathbb{R}} \subseteq {\rm PAT}_\mathbb{R}}$$ and conjectured to be different from $${{\rm PAT}_\mathbb{R}}$$ . We then complement this result and prove a non-trivial lower bound for $${{\rm IP}_\mathbb{R}}$$ . More precisely, we design interactive real protocols verifying function values for a large class of functions introduced by Koiran and Perifel and denoted by UniformVPSPACE $${^{0}.}$$ As a consequence, we show $${{\rm PAR}_\mathbb{R} \subseteq {\rm IP}_\mathbb{R}}$$ , which in particular implies co- $${{\rm NP}_\mathbb{R} \subseteq {\rm IP}_\mathbb{R}}$$ , and $${{\rm P}_\mathbb{R}^{Res} \subseteq {\rm IP}_\mathbb{R}}$$ , where Res denotes certain multivariate Resultant polynomials. Our proof techniques are guided by the question in how far Shamir’s classical proof can be used as well in the real number setting. Towards this aim results by Koiran and Perifel on UniformVPSPACE $${^{0}}$$ are extremely helpful.

Global analysis of b → sℓℓ anomalies

We present a detailed discussion of the current theoretical and experimental situation of the anomaly in the angular distribution of $B \to K^*(\to K\pi)\mu^+\mu^-$, observed at LHCb in the $1~\text{fb}^{-1}$ dataset and recently confirmed by the $3~\text{fb}^{-1}$ dataset. The impact of this data and other recent measurements on $b\to s\ell^+\ell^-$ transitions ($\ell=e,\mu$) is considered. We review the observables of interest, focusing on their theoretical uncertainties and their sensitivity to New Physics, based on an analysis employing the QCD factorisation approach including several sources of hadronic uncertainties (form factors, power corrections, charm-loop effects). We perform fits to New Physics contributions including experimental and theoretical correlations. The solution that we proposed in 2013 to solve the $B\to K^*\mu^+\mu^-$ anomaly, with a contribution ${\mathcal C}_9^{\rm NP}\simeq -1$, is confirmed and reinforced. A wider range of New-Physics scenarios with high significances (between 4 and 5 $\sigma$) emerges from the fit, some of them being particularly relevant for model building. More data is needed to discriminate among them conclusively. The inclusion of $b\to s e^+ e^-$ observables increases the significance of the favoured scenarios under the hypothesis of New Physics breaking lepton flavour universality. Several tests illustrate the robustness of our conclusions.

Z′model forb→sℓℓ¯flavor anomalies

We study the implications of flavour-changing neutral currents (FCNC's) in a model with the $SU(2)_l\times SU(2)_h\times U(1)_Y$ electroweak gauge symmetry for several anomalies appearing in $b\to s \ell\bar \ell$ induced $B$ decays in LHCb data. In this model, $SU(2)_l$ and $SU(2)_h$ govern the left-handed fermions in the first two generations and the third generation, respectively. The physical $Z$ and $Z'$ generate the $b\to s$ transition at tree level, leading to additional contributions to the $b \to s$ semileptonic operators ${\cal O}_{9,10}$. We find that although $B_s$-$\bar B_s$ mixing constrains the parameters severely, the model can produce values of ${\cal C}^{\rm NP}_{9,10}$ in the range determined by Descotes-Genon {\it et. al.} in Ref.~\cite{Descotes-Genon:2015uva} for this scenario to improve the global fit of observables in decays induced by the $b\to s \mu \bar \mu$ transition. The $Z'$ boson in this model also generates tree-level FCNC's for the leptonic interactions that can accommodate the experimental central value of $R_K = {\cal B}(B\to K \mu \bar \mu)/{\cal B}(B\to K e\bar e)=0.75$. In this case, the model predicts sizeable branching ratios for $B\to K e \bar \tau$, $B\to K \tau \bar e$, and an enhancement of $B\to K \tau \bar \tau$ with respect to its SM value.

Synthesis of Cross-Coupled Prototype Filters Including Resonant and Non-Resonant Nodes

In this paper, we present an approach to the synthesis of canonical cross-coupled prototype filters including resonant and non-resonant nodes (NRNs). The family of realizable topologies (including the folded and wheel configurations) is obtained through a recursive extraction technique and is characterized by all the couplings between adjacent nodes plus a number of cross-couplings between non-adjacent nodes (either resonant or non-resonant). The total number of distinct topologies that can be realized is ${\hbox{2}}^{({\rm np}-2)}$ with ${\rm np}$ order of the filter (i.e., number of poles). Some examples of synthesis are reported for illustrating the capabilities of the new proposed procedure. It is also shown how to de-normalize the synthesized low-pass prototype by means of the generalized coupling coefficients, which allow to extend the usual de-normalization procedure also to networks with NRNs.

RKand futureb→sℓℓphysics beyond the standard model opportunities

Flavor changing neutral current $|\Delta B|=|\Delta S|=1$ processes are sensitive to possible new physics at the electroweak scale and beyond, providing detailed information about flavor, chirality and Lorentz structure. Recently the LHCb collaboration announced a $2.6 \sigma$ deviation in the measurement of $R_K={\cal{B}}(\bar B \to \bar K \mu \mu)/{\cal{B}}(\bar B \to \bar K ee)$ from the standard model's prediction of lepton universality. We identify dimension six operators which could explain this deviation and study constraints from other measurements. Vector and axial-vector four-fermion operators with flavor structure $\bar s b \bar \ell \ell$ can provide a good description of the data. Tensor operators cannot describe the data. Pseudo-scalar and scalar operators only fit the data with some fine-tuning; they can be further probed with the $\bar B \to \bar K ee$ angular distribution. The data appears to point towards $C_9^{\rm NP \mu} = -C_{10}^{\rm NP \mu }<0$, an $SU(2)_{L}$ invariant direction in parameter space supported by $R_K$, the $\bar B \to \bar K^* \mu \mu$ forward-backward asymmetry and the $\bar B_s \to \mu \mu$ branching ratio, which is currently allowed to be smaller than the standard model prediction. We present two leptoquark models which can explain the FCNC data and give predictions for the LHC and rare decays.

Arthur and Merlin as Oracles

We study some problems solvable in deterministic polynomial time given oracle access to the (promise version of) Arthur–Merlin class. Our main results are the following: $$\circ\quad{\rm BPP}^{{\rm NP}}_{||} \subseteq {{\rm P}^{{{\rm pr}{\rm AM}}}_{||}}.$$ $$\circ\quad{{\rm S}_2^p} \subseteq {{\rm P}^{{{\rm pr}{\rm AM}}}}.$$ In addition to providing new upper bounds for the classes $${{{\rm S}_2^p}}$$ and $${{\rm BPP}^{{\rm NP}}_{||}}$$, these results are interesting from a derandomization perspective. In conjunction with the hitting set generator construction of Miltersen and Vinodchandran (Computational Complexity 14(3), 2005), we get that $${{{\rm S}_2^p} = {{\rm P}^{\rm NP}}}$$ and $${{\rm BPP}^{{\rm NP}}_{||} = {\rm P}^{{\rm NP}}_{||}}$$, under the hardness hypothesis associated with derandomizing the class AM. This gives an alternative proof of the same result obtained by Shaltiel and Umans (Computational Complexity 15(4), 2007). We also show that if NP has polynomial size circuits, then the polynomial time hierarchy (PH) collapses as PH = PprMA. Under the same hypothesis, we also derive a FPprMA algorithm for learning circuits for SAT; this improves the ZPPNP algorithm for the same problem by Bshouty et al. (JCSS 52(3), 1996). Finally, we design a FPprAM algorithm for the problem of finding near-optimal strategies for succinctly presented zero-sum games. For the same problem, Fortnow et al. (Computational Complexity 17(3), 2008a) described a ZPPNP algorithm. One advantage of our FPprAM algorithm is that it can be derandomized using the construction of Miltersen and Vinodchandran yielding a FPNP algorithm, under a hardness hypothesis used for derandomizing AM.

Nanofloating Gate Memory Devices Based on Controlled Metallic Nanoparticle-Embedded InGaZnO TFTs

In this letter, InGaZnO thin-film transistor (bottom-gate (n <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$+$</tex> </formula> Si) and top-contact structure)-based nanofloating gate memory devices were developed. These nonvolatile transistor memory devices contained self-assembled gold nanoparticles ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$ \hbox{Au}_{\rm NP}$</tex></formula> ) and exhibited good programmable memory characteristics according to the programming/erasing operations with large memory windows. The charge trapping in the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\hbox{Au}_{\rm NP}$</tex></formula> charge storage layers was responsible for the memory operations. The good endurance and data retention capability demonstrated by these memory devices make them suitable for nonvolatile memory applications. As this approach was based on the solution-processed controlled <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\hbox{Au}_{\rm NP}$</tex></formula> charge trapping layers and the low-temperature synthesized transparent oxide semiconductors, it has the potential for application in low-temperature-processed transparent nonvolatile memory devices.

Heavy fermions and two loop electroweak corrections to b → s + γ

Applying effective Lagrangian method and on-shell scheme, we analyze the electroweak corrections to the rare decay $b\rightarrow s+\gamma$ from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual charged gauge bosons or Higgs. At the decoupling limit where the virtual fermions in inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly when the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. Adopting the universal assumptions on the relevant couplings and mass spectrum of new physics, we find that the relative corrections from those two loop diagrams to the SM theoretical prediction on the branching ratio of $B\rightarrow X_{_s}\gamma$ can reach 5% as the energy scale of new physics $\Lambda_{_{\rm NP}}=200$ GeV.

Algorithms for Modular Counting of Roots of Multivariate Polynomials

Given a multivariate polynomial P(X1,…,Xn) over a finite field $\ensuremath {\mathbb {F}_{q}}$, let N(P) denote the number of roots over $\ensuremath {\mathbb {F}_{q}}^{n}$. The modular root counting problem is given a modulus r, to determine Nr(P)=N(P)mod r. We study the complexity of computing Nr(P), when the polynomial is given as a sum of monomials. We give an efficient algorithm to compute Nr(P) when the modulus r is a power of the characteristic of the field. We show that for all other moduli, the problem of computing Nr(P) is ${\rm NP}$-hard. We present some hardness results which imply that our algorithm is essentially optimal for prime fields. We show an equivalence between maximum-likelihood decoding for Reed-Solomon codes and a root-finding problem for symmetric polynomials.

Some Relations between Approximation Problems and PCPs over the Real Numbers

In [10] it was recently shown that $\mbox{\rm NP}_{\Bbb R} \subseteq \mbox{\rm PCP}_{\Bbb R}(\,{\it poly}, O(1)),$ that is the existence of transparent long proofs for $\mbox{\rm NP}_{\Bbb R}$ was established. The latter denotes the class of real number decision problems verifiable in polynomial time as introduced by Blum et al. [6]. The present paper is devoted to the question what impact a potential full real number $\mbox{\rm PCP}_{\Bbb R}$ theorem $\mbox{\rm NP}_{\Bbb R} = \mbox{\rm PCP}_{\Bbb R}(O(\log{n}), O(1))$ would have on approximation issues in the BSS model of computation. We study two natural optimization problems in the BSS model. The first, denoted by MAX-QPS, is related to polynomial systems; the other, MAX-q-CAP, deals with algebraic circuits. Our main results combine the PCP framework over ${\Bbb R}$ with approximation issues for these two problems. We also give a negative approximation result for a variant of the MAX-QPS problem.

Approximation and inapproximability results on balanced connected partitions of graphs

Graphs and Algorithms Let G=(V,E) be a connected graph with a weight function w: V \to \mathbbZ₊, and let q ≥q 2 be a positive integer. For X⊆ V, let w(X) denote the sum of the weights of the vertices in X. We consider the following problem on G: find a q-partition P=(V₁,V₂, \ldots, V_q) of V such that G[V_i] is connected (1≤q i≤q q) and P maximizes \rm min\w(V_i): 1≤q i≤q q\. This problem is called \textitMax Balanced Connected q-Partition and is denoted by BCP_q. We show that for q≥q 2 the problem BCP_q is NP-hard in the strong sense, even on q-connected graphs, and therefore does not admit a FPTAS, unless \rm P=\rm NP. We also show another inapproximability result for BCP₂ on arbitrary graphs. On q-connected graphs, for q=2 the best result is a \frac43-approximation algorithm obtained by Chleb\'ıková; for q=3 and q=4 we present 2-approximation algorithms. When q is not fixed (it is part of the instance), the corresponding problem is called \textitMax Balanced Connected Partition, and denoted as BCP. We show that BCP does not admit an approximation algorithm with ratio smaller than 6/5, unless \rm P=\rm NP.

The Complexity of Combinatorial Optimization Problems on d‐Dimensional Boxes

The MAXIMUM INDEPENDENT SET problem in d‐box graphs, i.e., in intersection graphs of axis‐parallel rectangles in $\mathbb{R}^d$, is known to be NP‐hard for any fixed $d\geq 2$. A challenging open problem is that of how closely the solution can be approximated by a polynomial time algorithm. For the restricted case of d‐boxes with bounded aspect ratio a PTAS exists [T. Erlebach, K. Jansen, and E. Seidel, SIAM J. Comput., 34 (2005), pp. 1302–1323]. In the general case no polynomial time algorithm with approximation ratio $o(\log^{d-1} n)$ for a set of n d‐boxes is known. In this paper we prove APX‐hardness of the MAXIMUM INDEPENDENT SET problem in d‐box graphs for any fixed $d\geq 3$. We give an explicit lower bound $\frac{245}{244}$ on efficient approximability for this problem unless $\PP=\text{\rm NP}$. Additionally, we provide a generic method how to prove APX‐hardness for other graph optimization problems in d‐box graphs for any fixed $d\geq 3$.

Power from Random Strings

We show that sets consisting of strings of high Kolmogorov complexity provide examples of sets that are complete for several complexity classes under probabilistic and nonuniform reductions. These sets are provably not complete under the usual many-one reductions. Let ${{R_{\rm C}}}, {{R_{\rm Kt}}}, {{R_{\rm KS}}}, {{R_{\rm KT}}}$ be the sets of strings x having complexity at least $|x|/2$, according to the usual Kolmogorov complexity measure ${\mbox{\rm C}}$, Levin's time-bounded Kolmogorov complexity ${\mbox{\rm Kt}}$ [L. Levin, Inform. and Control, 61 (1984), pp. 15-37], a space-bounded Kolmogorov measure ${\mbox{\rm KS}}$, and a new time-bounded Kolmogorov complexity measure ${\mbox{\rm KT}}$, respectively. Our main results are as follows: \begin{remunerate} \item ${{R_{\rm KS}}}$ and ${{R_{\rm Kt}}}$ are complete for ${{\rm{PSPACE}}}$ and {\mbox{\rm EXP}}, respectively, under ${\mbox{\rm P/poly}}$-truth-table reductions. Similar results hold for other classes with ${{\rm{PSPACE}}}$-robust Turing complete sets. \item ${\mbox{\rm EXP}} = {\mbox{\rm NP}}^{{{R_{\rm Kt}}}}.$ \item ${{\rm{PSPACE}}} = {\mbox{\rm ZPP}}^{{{R_{\rm KS}}}} \subseteq {\mbox{\rm P}}^{{{R_{\rm C}}}}$. \item The Discrete Log, Factoring, and several lattice problems are solvable in ${\mbox{\rm BPP}}^{{{R_{\rm KT}}}}$. \end{remunerate} Our hardness result for ${{\rm{PSPACE}}}$ gives rise to fairly natural problems that are complete for ${{\rm{PSPACE}}}$ under ${\mbox{$\leq^{\rm p}_{\rm T}$}}$ reductions, but not under ${\mbox{$\leq^{\rm log}_{\rm m}$}}$ reductions. Our techniques also allow us to show that all computably enumerable sets are reducible to ${{R_{\rm C}}}$ via ${\mbox{\rm P/poly}}$-truth-table reductions. This provides the first "efficient" reduction of the halting problem to ${{R_{\rm C}}}$.

Redistribution of Ni implanted into InP

The redistribution of Ni in InP is studied by annealing samples of InP implanted with 0.9 MeV Ni at 60o angle of ion incidence with respect to target surface normal as a function of dose (8.5×10 12 −4.5×10 15 cm −2 ). Ni profiles are measured by secondary ion mass spectrometry (SIMS) and implantation induced damage by Rutherford backscattering spectrometry in channeling (RBS/C) condition. The highest dose sample is characterised by remarkable Ni accumulation near the surface (at ∼ $0.3R_{\rm np}$ ) that has not been observed earlier along with two other distinct accumulation zones at R np + $\Delta R_{\rm np}$ and $2.2R_{\rm np}$ after annealing at 650 °C for 30 min. Here, R np is the normal component of the projected range for oblique angle bombardment.