2,451 research outputs found
Decidability of All Minimal Models (Revised Version - 2012)
This unpublished note is an alternate, shorter (and hopefully more readable)
proof of the decidability of all minimal models. The decidability follows from
a proof of the existence of a cellular term in each observational equivalence
class of a minimal model
When Can We Answer Queries Using Result-Bounded Data Interfaces?
We consider answering queries on data available through access methods, that
provide lookup access to the tuples matching a given binding. Such interfaces
are common on the Web; further, they often have bounds on how many results they
can return, e.g., because of pagination or rate limits. We thus study
result-bounded methods, which may return only a limited number of tuples. We
study how to decide if a query is answerable using result-bounded methods,
i.e., how to compute a plan that returns all answers to the query using the
methods, assuming that the underlying data satisfies some integrity
constraints. We first show how to reduce answerability to a query containment
problem with constraints. Second, we show "schema simplification" theorems
describing when and how result bounded services can be used. Finally, we use
these theorems to give decidability and complexity results about answerability
for common constraint classes.Comment: 65 pages; journal version of the PODS'18 paper arXiv:1706.0793
Decidability of higher-order matching
We show that the higher-order matching problem is decidable using a
game-theoretic argument.Comment: appears in LMCS (Logical Methods in Computer Science
When Can We Answer Queries Using Result-Bounded Data Interfaces?
We consider answering queries where the underlying data is available only
over limited interfaces which provide lookup access to the tuples matching a
given binding, but possibly restricting the number of output tuples returned.
Interfaces imposing such "result bounds" are common in accessing data via the
web. Given a query over a set of relations as well as some integrity
constraints that relate the queried relations to the data sources, we examine
the problem of deciding if the query is answerable over the interfaces; that
is, whether there exists a plan that returns all answers to the query, assuming
the source data satisfies the integrity constraints.
The first component of our analysis of answerability is a reduction to a
query containment problem with constraints. The second component is a set of
"schema simplification" theorems capturing limitations on how interfaces with
result bounds can be useful to obtain complete answers to queries. These
results also help to show decidability for the containment problem that
captures answerability, for many classes of constraints. The final component in
our analysis of answerability is a "linearization" method, showing that query
containment with certain guarded dependencies -- including those that emerge
from answerability problems -- can be reduced to query containment for a
well-behaved class of linear dependencies. Putting these components together,
we get a detailed picture of how to check answerability over result-bounded
services.Comment: 45 pages, 2 tables, 43 references. Complete version with proofs of
the PODS'18 paper. The main text of this paper is almost identical to the
PODS'18 except that we have fixed some small mistakes. Relative to the
earlier arXiv version, many errors were corrected, and some terminology has
change
Decision Problems for Petri Nets with Names
We prove several decidability and undecidability results for nu-PN, an
extension of P/T nets with pure name creation and name management. We give a
simple proof of undecidability of reachability, by reducing reachability in
nets with inhibitor arcs to it. Thus, the expressive power of nu-PN strictly
surpasses that of P/T nets. We prove that nu-PN are Well Structured Transition
Systems. In particular, we obtain decidability of coverability and termination,
so that the expressive power of Turing machines is not reached. Moreover, they
are strictly Well Structured, so that the boundedness problem is also
decidable. We consider two properties, width-boundedness and depth-boundedness,
that factorize boundedness. Width-boundedness has already been proven to be
decidable. We prove here undecidability of depth-boundedness. Finally, we
obtain Ackermann-hardness results for all our decidable decision problems.Comment: 20 pages, 7 figure
Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility
Word equations are a crucial element in the theoretical foundation of
constraint solving over strings, which have received a lot of attention in
recent years. A word equation relates two words over string variables and
constants. Its solution amounts to a function mapping variables to constant
strings that equate the left and right hand sides of the equation. While the
problem of solving word equations is decidable, the decidability of the problem
of solving a word equation with a length constraint (i.e., a constraint
relating the lengths of words in the word equation) has remained a
long-standing open problem. In this paper, we focus on the subclass of
quadratic word equations, i.e., in which each variable occurs at most twice. We
first show that the length abstractions of solutions to quadratic word
equations are in general not Presburger-definable. We then describe a class of
counter systems with Presburger transition relations which capture the length
abstraction of a quadratic word equation with regular constraints. We provide
an encoding of the effect of a simple loop of the counter systems in the theory
of existential Presburger Arithmetic with divisibility (PAD). Since PAD is
decidable, we get a decision procedure for quadratic words equations with
length constraints for which the associated counter system is \emph{flat}
(i.e., all nodes belong to at most one cycle). We show a decidability result
(in fact, also an NP algorithm with a PAD oracle) for a recently proposed
NP-complete fragment of word equations called regular-oriented word equations,
together with length constraints. Decidability holds when the constraints are
additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page
Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids
There have been several attempts to extend the notion of conjugacy from
groups to monoids. The aim of this paper is study the decidability and
independence of conjugacy problems for three of these notions (which we will
denote by , , and ) in certain classes of finitely
presented monoids. We will show that in the class of polycyclic monoids,
-conjugacy is "almost" transitive, is strictly included in
, and the - and -conjugacy problems are decidable with linear
compexity. For other classes of monoids, the situation is more complicated. We
show that there exists a monoid defined by a finite complete presentation
such that the -conjugacy problem for is undecidable, and that for
finitely presented monoids, the -conjugacy problem and the word problem are
independent, as are the -conjugacy and -conjugacy problems.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1503.0091
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