10,333 research outputs found
Minsky machines and algorithmic problems
This is a survey of using Minsky machines to study algorithmic problems in
semigroups, groups and other algebraic systems.Comment: 19 page
On the time complexity of 2-tag systems and small universal Turing machines
We show that 2-tag systems efficiently simulate Turing machines. As a
corollary we find that the small universal Turing machines of Rogozhin, Minsky
and others simulate Turing machines in polynomial time. This is an exponential
improvement on the previously known simulation time overhead and improves a
forty year old result in the area of small universal Turing machines.Comment: Slightly expanded and updated from conference versio
Undecidability of Multiplicative Subexponential Logic
Subexponential logic is a variant of linear logic with a family of
exponential connectives--called subexponentials--that are indexed and arranged
in a pre-order. Each subexponential has or lacks associated structural
properties of weakening and contraction. We show that classical propositional
multiplicative linear logic extended with one unrestricted and two incomparable
linear subexponentials can encode the halting problem for two register Minsky
machines, and is hence undecidable.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441
Dense-choice Counter Machines revisited
This paper clarifies the picture about Dense-choice Counter Machines, which
have been less studied than (discrete) Counter Machines. We revisit the
definition of "Dense Counter Machines" so that it now extends (discrete)
Counter Machines, and we provide new undecidability and decidability results.
Using the first-order additive mixed theory of reals and integers, we give a
logical characterization of the sets of configurations reachable by
reversal-bounded Dense-choice Counter Machines
Temporal logic with predicate abstraction
A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but
with predicate abstraction mechanism and equality is considered. The models of
LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible
constants) moving over the elements of some (possibly infinite) domain. This
allows to use LTL_{\lambda,=} for the specification of dynamic systems using
some resources, such as processes using memory locations, mobile agents
occupying some sites, etc. On the other hand we show that LTL_{\lambda,=} is
not recursively axiomatizable and, therefore, fully automated verification of
LTL_{\lambda,=} specifications is not, in general, possible.Comment: 14 pages, 4 figure
О разрешимости проблем ограниченности для счетчиковых машин Минского
In the paper the decidability of boundedness problems for counter Minsky machines is investigated. It is proved, that for Minsky machines with two counters the boundedness is partial decidable, but for the total boundedness problem does not even exist a semidecision algorithm. On the other hand, for one-counter Minsky machines all these problems are polinomial (quantitatively of local machine states) decidable.Исследуется разрешимость проблем ограниченности для счетчиковых машин Минского. Доказывается, что для машин Минского с двумя счетчиками проблема ограниченности лишь частично разрешима, а проблема тотальной ограниченности не является даже частично разрешимой. Для односчет-чиковых машин Минского указанные проблемы разрешимы за время, полиномиально зависящее от общего количества локальных состояний счетчиковой машины
On the boundaries of solvability and unsolvability in tag systems. Theoretical and Experimental Results
Several older and more recent results on the boundaries of solvability and
unsolvability in tag systems are surveyed. Emphasis will be put on the
significance of computer experiments in research on very small tag systems
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