1,805 research outputs found
On the equivalence, containment, and covering problems for the regular and context-free languages
We consider the complexity of the equivalence and containment problems for regular expressions and context-free grammars, concentrating on the relationship between complexity and various language properties. Finiteness and boundedness of languages are shown to play important roles in the complexity of these problems. An encoding into grammars of Turing machine computations exponential in the size of the grammar is used to prove several exponential lower bounds. These lower bounds include exponential time for testing equivalence of grammars generating finite sets, and exponential space for testing equivalence of non-self-embedding grammars. Several problems which might be complex because of this encoding are shown to simplify for linear grammars. Other problems considered include grammatical covering and structural equivalence for right-linear, linear, and arbitrary grammars
Measurement of the mass difference and the binding energy of the hypertriton and antihypertriton
According to the CPT theorem, which states that the combined operation of
charge conjugation, parity transformation and time reversal must be conserved,
particles and their antiparticles should have the same mass and lifetime but
opposite charge and magnetic moment. Here, we test CPT symmetry in a nucleus
containing a strange quark, more specifically in the hypertriton. This
hypernucleus is the lightest one yet discovered and consists of a proton, a
neutron, and a hyperon. With data recorded by the STAR
detector{\cite{TPC,HFT,TOF}} at the Relativistic Heavy Ion Collider, we measure
the hyperon binding energy for the hypertriton, and
find that it differs from the widely used value{\cite{B_1973}} and from
predictions{\cite{2019_weak, 1995_weak, 2002_weak, 2014_weak}}, where the
hypertriton is treated as a weakly bound system. Our results place stringent
constraints on the hyperon-nucleon interaction{\cite{Hammer2002,
STAR-antiH3L}}, and have implications for understanding neutron star interiors,
where strange matter may be present{\cite{Chatterjee2016}}. A precise
comparison of the masses of the hypertriton and the antihypertriton allows us
to test CPT symmetry in a nucleus with strangeness for the first time, and we
observe no deviation from the expected exact symmetry
- …