2,852 research outputs found
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure
String languages recognizable in (deterministic) log-space are characterized
either by two-way (deterministic) multi-head automata, or following Immerman,
by first-order logic with (deterministic) transitive closure. Here we elaborate
this result, and match the number of heads to the arity of the transitive
closure. More precisely, first-order logic with k-ary deterministic transitive
closure has the same power as deterministic automata walking on their input
with k heads, additionally using a finite set of nested pebbles. This result is
valid for strings, ordered trees, and in general for families of graphs having
a fixed automaton that can be used to traverse the nodes of each of the graphs
in the family. Other examples of such families are grids, toruses, and
rectangular mazes. For nondeterministic automata, the logic is restricted to
positive occurrences of transitive closure.
The special case of k=1 for trees, shows that single-head deterministic
tree-walking automata with nested pebbles are characterized by first-order
logic with unary deterministic transitive closure. This refines our earlier
result that placed these automata between first-order and monadic second-order
logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur
A Note on a New Class of APCol Systems
We introduce a new acceptance mode for APCol systems (Automaton-like P
colonies), variants of P colonies where the environment of the agents is given by a string
and during functioning the agents change their own states and process the string similarly
to automata. In case of the standard variant, the string is accepted if it can be reduced
to the empty word. In this paper, we de ne APCol systems where the agents verify their
environment, a model resembling multihead nite automata. In this case, a string of
length n is accepted if during every halting computation the length of the environmental
string in the con gurations does not change and in the course of the computation every
agent applies a rule to a symbol on position i of some of the environmental strings for
every i, 1 < i < n at least once. We show that these verifying APCol systems simulate
one-way multihead nite automata
Aperiodic tilings and entropy
In this paper we present a construction of Kari-Culik aperiodic tile set -
the smallest known until now. With the help of this construction, we prove that
this tileset has positive entropy. We also explain why this result was not
expected
Small-world behavior in a system of mobile elements
We analyze the propagation of activity in a system of mobile automata. A
number r L^d of elements move as random walkers on a lattice of dimension d,
while with a small probability p they can jump to any empty site in the system.
We show that this system behaves as a Dynamic Small-World (DSW) and present
analytic and numerical results for several quantities. Our analysis shows that
the persistence time T* (equivalent to the persistence size L* of small-world
networks) scales as T* ~ (r p)^(-t), with t = 1/(d+1).Comment: To appear in Europhysics Letter
Jumping Finite Automata for Tweet Comprehension
Every day, over one billion social media text messages are generated worldwide, which provides abundant information that can lead to improvements in lives of people through evidence-based decision making. Twitter is rich in such data but there are a number of technical challenges in comprehending tweets including ambiguity of the language used in tweets which is exacerbated in under resourced languages. This paper presents an approach based on Jumping Finite Automata for automatic comprehension of tweets. We construct a WordNet for the language of Kenya (WoLK) based on analysis of tweet structure, formalize the space of tweet variation and abstract the space on a Finite Automata. In addition, we present a software tool called Automata-Aided Tweet Comprehension (ATC) tool that takes raw tweets as input, preprocesses, recognise the syntax and extracts semantic information to 86% success rate
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