3,366 research outputs found
Passively Mobile Communicating Logarithmic Space Machines
We propose a new theoretical model for passively mobile Wireless Sensor
Networks. We call it the PALOMA model, standing for PAssively mobile
LOgarithmic space MAchines. The main modification w.r.t. the Population
Protocol model is that agents now, instead of being automata, are Turing
Machines whose memory is logarithmic in the population size n. Note that the
new model is still easily implementable with current technology. We focus on
complete communication graphs. We define the complexity class PLM, consisting
of all symmetric predicates on input assignments that are stably computable by
the PALOMA model. We assume that the agents are initially identical.
Surprisingly, it turns out that the PALOMA model can assign unique consecutive
ids to the agents and inform them of the population size! This allows us to
give a direct simulation of a Deterministic Turing Machine of O(nlogn) space,
thus, establishing that any symmetric predicate in SPACE(nlogn) also belongs to
PLM. We next prove that the PALOMA model can simulate the Community Protocol
model, thus, improving the previous lower bound to all symmetric predicates in
NSPACE(nlogn). Going one step further, we generalize the simulation of the
deterministic TM to prove that the PALOMA model can simulate a Nondeterministic
TM of O(nlogn) space. Although providing the same lower bound, the important
remark here is that the bound is now obtained in a direct manner, in the sense
that it does not depend on the simulation of a TM by a Pointer Machine.
Finally, by showing that a Nondeterministic TM of O(nlogn) space decides any
language stably computable by the PALOMA model, we end up with an exact
characterization for PLM: it is precisely the class of all symmetric predicates
in NSPACE(nlogn).Comment: 22 page
One-Tape Turing Machine Variants and Language Recognition
We present two restricted versions of one-tape Turing machines. Both
characterize the class of context-free languages. In the first version,
proposed by Hibbard in 1967 and called limited automata, each tape cell can be
rewritten only in the first visits, for a fixed constant .
Furthermore, for deterministic limited automata are equivalent to
deterministic pushdown automata, namely they characterize deterministic
context-free languages. Further restricting the possible operations, we
consider strongly limited automata. These models still characterize
context-free languages. However, the deterministic version is less powerful
than the deterministic version of limited automata. In fact, there exist
deterministic context-free languages that are not accepted by any deterministic
strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of
the September 2015 issue of SIGACT New
Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis
The classic approaches to synthesize a reactive system from a linear temporal
logic (LTL) specification first translate the given LTL formula to an
equivalent omega-automaton and then compute a winning strategy for the
corresponding omega-regular game. To this end, the obtained omega-automata have
to be (pseudo)-determinized where typically a variant of Safra's
determinization procedure is used. In this paper, we show that this
determinization step can be significantly improved for tool implementations by
replacing Safra's determinization by simpler determinization procedures. In
particular, we exploit (1) the temporal logic hierarchy that corresponds to the
well-known automata hierarchy consisting of safety, liveness, Buechi, and
co-Buechi automata as well as their boolean closures, (2) the non-confluence
property of omega-automata that result from certain translations of LTL
formulas, and (3) symbolic implementations of determinization procedures for
the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular,
we present convincing experimental results that demonstrate the practical
applicability of our new synthesis procedure
Alternation-Trading Proofs, Linear Programming, and Lower Bounds
A fertile area of recent research has demonstrated concrete polynomial time
lower bounds for solving natural hard problems on restricted computational
models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path,
Mod6-SAT, Majority-of-Majority-SAT, and Tautologies, to name a few. The proofs
of these lower bounds follow a certain proof-by-contradiction strategy that we
call alternation-trading. An important open problem is to determine how
powerful such proofs can possibly be.
We propose a methodology for studying these proofs that makes them amenable
to both formal analysis and automated theorem proving. We prove that the search
for better lower bounds can often be turned into a problem of solving a large
series of linear programming instances. Implementing a small-scale theorem
prover based on this result, we extract new human-readable time lower bounds
for several problems. This framework can also be used to prove concrete
limitations on the current techniques.Comment: To appear in STACS 2010, 12 page
The parameterized space complexity of model-checking bounded variable first-order logic
The parameterized model-checking problem for a class of first-order sentences
(queries) asks to decide whether a given sentence from the class holds true in
a given relational structure (database); the parameter is the length of the
sentence. We study the parameterized space complexity of the model-checking
problem for queries with a bounded number of variables. For each bound on the
quantifier alternation rank the problem becomes complete for the corresponding
level of what we call the tree hierarchy, a hierarchy of parameterized
complexity classes defined via space bounded alternating machines between
parameterized logarithmic space and fixed-parameter tractable time. We observe
that a parameterized logarithmic space model-checker for existential bounded
variable queries would allow to improve Savitch's classical simulation of
nondeterministic logarithmic space in deterministic space .
Further, we define a highly space efficient model-checker for queries with a
bounded number of variables and bounded quantifier alternation rank. We study
its optimality under the assumption that Savitch's Theorem is optimal
The Nondeterministic Waiting Time Algorithm: A Review
We present briefly the Nondeterministic Waiting Time algorithm. Our technique
for the simulation of biochemical reaction networks has the ability to mimic
the Gillespie Algorithm for some networks and solutions to ordinary
differential equations for other networks, depending on the rules of the
system, the kinetic rates and numbers of molecules. We provide a full
description of the algorithm as well as specifics on its implementation. Some
results for two well-known models are reported. We have used the algorithm to
explore Fas-mediated apoptosis models in cancerous and HIV-1 infected T cells
Finding the Median (Obliviously) with Bounded Space
We prove that any oblivious algorithm using space to find the median of a
list of integers from requires time . This bound also applies to the problem of determining whether the median
is odd or even. It is nearly optimal since Chan, following Munro and Raman, has
shown that there is a (randomized) selection algorithm using only
registers, each of which can store an input value or -bit counter,
that makes only passes over the input. The bound also implies
a size lower bound for read-once branching programs computing the low order bit
of the median and implies the analog of for length oblivious branching programs
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
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