Computational Complexity of Synchronization under Regular Commutative Constraints

Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full classification of the computational complexity of the constraint synchronization problem. Depending on the constraint language, our problem becomes PSPACE-complete, NP-complete or polynomial time solvable. In addition, we derive a polynomial time decision procedure for the complexity of the constraint synchronization problem, given some constraint automaton accepting a commutative language as input.Comment: Published in COCOON 2020 (The 26th International Computing and Combinatorics Conference); 2nd version is update of the published version and 1st version; both contain a minor error, the assumption of maximality in the NP-c and PSPACE-c results (propositions 5 & 6) is missing, and of incomparability of the vectors in main theorem; fixed in this version. See (new) discussion after main theore

DFAs and PFAs with Long Shortest Synchronizing Word Length

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 6$, without bounds on the number of symbols. For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation.Comment: 16 pages, 2 figures source code adde

Using Sat solvers for synchronization issues in partial deterministic automata

We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that this approach gives satisfactory results for automata with up to 100 states even if very modest computational resources are used.Comment: 15 pages, 3 figure

Synchronization Problems in Automata without Non-trivial Cycles

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizing set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889. Conference version was published at CIAA 2017, LNCS vol. 10329, pages 188-200, 201

Checking Whether an Automaton Is Monotonic Is NP-complete

An automaton is monotonic if its states can be arranged in a linear order that is preserved by the action of every letter. We prove that the problem of deciding whether a given automaton is monotonic is NP-complete. The same result is obtained for oriented automata, whose states can be arranged in a cyclic order. Moreover, both problems remain hard under the restriction to binary input alphabets.Comment: 13 pages, 4 figures. CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_2

Search for Axionlike and Scalar Particles with the NA64 Experiment

We carried out a model-independent search for light scalar (s) and pseudoscalar axionlike (a) particles that couple to two photons by using the high-energy CERN SPS H4 electron beam. The new particles, if they exist, could be produced through the Primakoff effect in interactions of hard bremsstrahlung photons generated by 100 GeV electrons in the NA64 active dump with virtual photons provided by the nuclei of the dump. The a(s) would penetrate the downstream HCAL module, serving as shielding, and would be observed either through their $a(s)\to\gamma \gamma$ decay in the rest of the HCAL detector or as events with large missing energy if the a(s) decays downstream of the HCAL. This method allows for the probing the a(s) parameter space, including those from generic axion models, inaccessible to previous experiments. No evidence of such processes has been found from the analysis of the data corresponding to $2.84\times10^{11}$ electrons on target allowing to set new limits on the $a(s)\gamma\gamma$-coupling strength for a(s) masses below 55 MeV.Comment: This publication is dedicated to the memory of our colleague Danila Tlisov. 7 pages, 5 figures, revised version accepted for publication in Phys. Rev. Let

Domain Swapping and Different Oligomeric States for the Complex Between Calmodulin and the Calmodulin-Binding Domain of Calcineurin A

BACKGROUND: Calmodulin (CaM) is a ubiquitously expressed calcium sensor that engages in regulatory interactions with a large number of cellular proteins. Previously, a unique mode of CaM target recognition has been observed in the crystal structure of a complex between CaM and the CaM-binding domain of calcineurin A. METHODOLOGY/PRINCIPAL FINDINGS: We have solved a high-resolution crystal structure of a complex between CaM and the CaM-binding domain of calcineurin A in a novel crystal form, which shows a dimeric assembly of calmodulin, as observed before in the crystal state. We note that the conformation of CaM in this complex is very similar to that of unliganded CaM, and a detailed analysis revels that the CaM-binding motif in calcineurin A is of a novel '1-11' type. However, using small-angle X-ray scattering (SAXS), we show that the complex is fully monomeric in solution, and a structure of a canonically collapsed CaM-peptide complex can easily be fitted into the SAXS data. This result is also supported by size exclusion chromatography, where the addition of the ligand peptide decreases the apparent size of CaM. In addition, we studied the energetics of binding by isothermal titration calorimetry and found them to closely resemble those observed previously for ligand peptides from CaM-dependent kinases. CONCLUSIONS/SIGNIFICANCE: Our results implicate that CaM can also form a complex with the CaM-binding domain of calcineurin in a 1 ratio 1 stoichiometry, in addition to the previously observed 2 ratio 2 arrangement in the crystal state. At the structural level, going from 2 ratio 2 association to two 1 ratio 1 complexes will require domain swapping in CaM, accompanied by the characteristic bending of the central linker helix between the two lobes of CaM

Lectin-like bacteriocins from pseudomonas spp. utilise D-rhamnose containing lipopolysaccharide as a cellular receptor

Lectin-like bacteriocins consist of tandem monocot mannose-binding domains and display a genus-specific killing activity. Here we show that pyocin L1, a novel member of this family from Pseudomonas aeruginosa, targets susceptible strains of this species through recognition of the common polysaccharide antigen (CPA) of P. aeruginosa lipopolysaccharide that is predominantly a homopolymer of d-rhamnose. Structural and biophysical analyses show that recognition of CPA occurs through the C-terminal carbohydrate-binding domain of pyocin L1 and that this interaction is a prerequisite for bactericidal activity. Further to this, we show that the previously described lectin-like bacteriocin putidacin L1 shows a similar carbohydrate-binding specificity, indicating that oligosaccharides containing d-rhamnose and not d-mannose, as was previously thought, are the physiologically relevant ligands for this group of bacteriocins. The widespread inclusion of d-rhamnose in the lipopolysaccharide of members of the genus Pseudomonas explains the unusual genus-specific activity of the lectin-like bacteriocins

Mismatch Repair–Independent Increase in Spontaneous Mutagenesis in Yeast Lacking Non-Essential Subunits of DNA Polymerase ε

Yeast DNA polymerase ε (Pol ε) is a highly accurate and processive enzyme that participates in nuclear DNA replication of the leading strand template. In addition to a large subunit (Pol2) harboring the polymerase and proofreading exonuclease active sites, Pol ε also has one essential subunit (Dpb2) and two smaller, non-essential subunits (Dpb3 and Dpb4) whose functions are not fully understood. To probe the functions of Dpb3 and Dpb4, here we investigate the consequences of their absence on the biochemical properties of Pol ε in vitro and on genome stability in vivo. The fidelity of DNA synthesis in vitro by purified Pol2/Dpb2, i.e. lacking Dpb3 and Dpb4, is comparable to the four-subunit Pol ε holoenzyme. Nonetheless, deletion of DPB3 and DPB4 elevates spontaneous frameshift and base substitution rates in vivo, to the same extent as the loss of Pol ε proofreading activity in a pol2-4 strain. In contrast to pol2-4, however, the dpb3Δdpb4Δ does not lead to a synergistic increase of mutation rates with defects in DNA mismatch repair. The increased mutation rate in dpb3Δdpb4Δ strains is partly dependent on REV3, as well as the proofreading capacity of Pol δ. Finally, biochemical studies demonstrate that the absence of Dpb3 and Dpb4 destabilizes the interaction between Pol ε and the template DNA during processive DNA synthesis and during processive 3′ to 5′exonucleolytic degradation of DNA. Collectively, these data suggest a model wherein Dpb3 and Dpb4 do not directly influence replication fidelity per se, but rather contribute to normal replication fork progression. In their absence, a defective replisome may more frequently leave gaps on the leading strand that are eventually filled by Pol ζ or Pol δ, in a post-replication process that generates errors not corrected by the DNA mismatch repair system

Improved exclusion limit for light dark matter from e+e- annihilation in NA64

The current most stringent constraints for the existence of sub-GeV dark matter coupling to Standard Model via a massive vector boson A′ were set by the NA64 experiment for the mass region mA′≲250 MeV, by analyzing data from the interaction of 2.84×1011 100-GeV electrons with an active thick target and searching for missing-energy events. In this work, by including A′ production via secondary positron annihilation with atomic electrons, we extend these limits in the 200-300 MeV region by almost an order of magnitude, touching for the first time the dark matter relic density constrained parameter combinations. Our new results demonstrate the power of the resonant annihilation process in missing energy dark-matter searches, paving the road to future dedicated e+ beam efforts