23 research outputs found
Revisiting Synthesis for One-Counter Automata
We study the (parameter) synthesis problem for one-counter automata with
parameters. One-counter automata are obtained by extending classical
finite-state automata with a counter whose value can range over non-negative
integers and be tested for zero. The updates and tests applicable to the
counter can further be made parametric by introducing a set of integer-valued
variables called parameters. The synthesis problem for such automata asks
whether there exists a valuation of the parameters such that all infinite runs
of the automaton satisfy some omega-regular property. Lechner showed that (the
complement of) the problem can be encoded in a restricted one-alternation
fragment of Presburger arithmetic with divisibility. In this work (i) we argue
that said fragment, called AERPADPLUS, is unfortunately undecidable.
Nevertheless, by a careful re-encoding of the problem into a decidable
restriction of AERPADPLUS, (ii) we prove that the synthesis problem is
decidable in general and in N2EXP for several fixed omega-regular properties.
Finally, (iii) we give a polynomial-space algorithm for the special case of the
problem where parameters can only be used in tests, and not updates, of the
counter
Revisiting Parameter Synthesis for One-Counter Automata
We study the synthesis problem for one-counter automata with parameters. One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero. The updates and tests applicable to the counter can further be made parametric by introducing a set of integer-valued variables called parameters. The synthesis problem for such automata asks whether there exists a valuation of the parameters such that all infinite runs of the automaton satisfy some ?-regular property. Lechner showed that (the complement of) the problem can be encoded in a restricted one-alternation fragment of Presburger arithmetic with divisibility. In this work (i) we argue that said fragment, called ??_RPAD^+, is unfortunately undecidable. Nevertheless, by a careful re-encoding of the problem into a decidable restriction of ??_RPAD^+, (ii) we prove that the synthesis problem is decidable in general and in 2NEXP for several fixed ?-regular properties. Finally, (iii) we give polynomial-space algorithms for the special cases of the problem where parameters can only be used in counter tests
Parikh One-Counter Automata
Counting abilities in finite automata are traditionally provided by two orthogonal extensions: adding a single counter that can be tested for zeroness at any point, or adding ?-valued counters that are tested for equality only at the end of runs. In this paper, finite automata extended with both types of counters are introduced. They are called Parikh One-Counter Automata (POCA): the "Parikh" part referring to the evaluation of counters at the end of runs, and the "One-Counter" part to the single counter that can be tested during runs.
Their expressiveness, in the deterministic and nondeterministic variants, is investigated; it is shown in particular that there are deterministic POCA languages that cannot be expressed without nondeterminism in the original models. The natural decision problems are also studied; strikingly, most of them are no harder than in the original models. A parametric version of nonemptiness is also considered
Reachability games with relaxed energy constraints
We study games with reachability objectives under energy constraints. We first prove that under strict energy constraints (either only lower-bound constraint or interval constraint), those games are LOGSPACE-equivalent to energy games with the same energy constraints but without reachability objective (i.e., for infinite runs). We then consider two relaxations of the upper-bound constraints (while keeping the lower-bound constraint strict): in the first one, called weak upper bound, the upper bound is absorbing, i.e., when the upper bound is reached, the extra energy is not stored; in the second one, we allow for temporary violations of the upper bound, imposing limits on the number or on the amount of violations. We prove that when considering weak upper bound, reachability objectives require memory, but can still be solved in polynomial-time for one-player arenas ; we prove that they are in coNP in the two-player setting. Allowing for bounded violations makes the problem PSPACE-complete for one-player arenas and EXPTIME-complete for two players. We then address the problem of existence of bounds for a given arena. We show that with reachability objectives, existence can be a simpler problem than the game itself, and conversely that with infinite games, existence can be harder
General Relativistic effects on the conversion of nuclear to two-flavour quark matter in compact stars
We investigate the General Relativistic (GR) effects on the conversion from
nuclear to two-flavour quark matter in compact stars, both static as well as
rotating. We find that GR effects lead to qualitative differences in rotating
stars, indicating the inadequacy of non-relativistic (NR) or even Special
Relativistic (SR) treatments for these cases.Comment: 4 pages, 4 figure
Synthesizing Efficiently Monitorable Formulas in Metric Temporal Logic
In runtime verification, manually formalizing a specification for monitoring
system executions is a tedious and error-prone process. To address this issue,
we consider the problem of automatically synthesizing formal specifications
from system executions. To demonstrate our approach, we consider the popular
specification language Metric Temporal Logic (MTL), which is particularly
tailored towards specifying temporal properties for cyber-physical systems
(CPS). Most of the classical approaches for synthesizing temporal logic
formulas aim at minimizing the size of the formula. However, for efficiency in
monitoring, along with the size, the amount of "lookahead" required for the
specification becomes relevant, especially for safety-critical applications. We
formalize this notion and devise a learning algorithm that synthesizes concise
formulas having bounded lookahead. To do so, our algorithm reduces the
synthesis task to a series of satisfiability problems in Linear Real Arithmetic
(LRA) and generates MTL formulas from their satisfying assignments. The
reduction uses a novel encoding of a popular MTL monitoring procedure using
LRA. Finally, we implement our algorithm in a tool called TEAL and demonstrate
its ability to synthesize efficiently monitorable MTL formulas in a CPS
application
The conversion of Neutron star to Strange star : A two step process
The conversion of neutron matter to strange matter in a neutron star have
been studied as a two step process. In the first step, the nuclear matter gets
converted to two flavour quark matter. The conversion of two flavour to three
flavour strange matter takes place in the second step. The first process is
analysed with the help of equations of state and hydrodynamical equations,
whereas, in the second process, non-leptonic weak interaction plays the main
role. Velocities and the time of travel through the star of these two
conversion fronts have been analysed and compared.Comment: 18 pages including 9 figure
Solving relativistic hydrodynamic equation in presence of magnetic field for phase transition in a neutron star
Hadronic to quark matter phase transition may occur inside neutron stars (NS)
having central densities of the order of 3-10 times normal nuclear matter
saturation density (). The transition is expected to be a two-step
process; transition from hadronic to 2-flavour matter and two-flavour to
equilibrated charge neutral three-flavour matter. In this paper we
concentrate on the first step process and solve the relativistic hydrodynamic
equations for the conversion front in presence of high magnetic field. Lorentz
force due to magnetic field is included in the energy momentum tensor by
averaging over the polar angles. We find that for an initial dipole
configuration of the magnetic field with a sufficiently high value at the
surface, velocity of the front increases considerably.Comment: 16 pages, 4 figures, same as published version of JPG, J. Phys. G:
Nucl. Part. Phys. 39 (2012) 09520