376,227 research outputs found
Feasible Automata for Two-Variable Logic with Successor on Data Words
We introduce an automata model for data words, that is words that carry at
each position a symbol from a finite alphabet and a value from an unbounded
data domain. The model is (semantically) a restriction of data automata,
introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data
automata. It is strictly less expressive than data automata and the expressive
power is incomparable with register automata. The expressive power of weak data
automata corresponds exactly to existential monadic second order logic with
successor +1 and data value equality \sim, EMSO2(+1,\sim). It follows from
previous work, David, et. al. in 2010, that the nonemptiness problem for weak
data automata can be decided in 2-NEXPTIME. Furthermore, we study weak B\"uchi
automata on data omega-strings. They can be characterized by the extension of
EMSO2(+1,\sim) with existential quantifiers for infinite sets. Finally, the
same complexity bound for its nonemptiness problem is established by a
nondeterministic polynomial time reduction to the nonemptiness problem of weak
data automata.Comment: 21 page
Two-Variable Logic with Two Order Relations
It is shown that the finite satisfiability problem for two-variable logic
over structures with one total preorder relation, its induced successor
relation, one linear order relation and some further unary relations is
EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures
that do not include the induced successor relation. As a special case, the
EXPSPACE upper bound applies to two-variable logic over structures with two
linear orders. A further consequence is that satisfiability of two-variable
logic over data words with a linear order on positions and a linear order and
successor relation on the data is decidable in EXPSPACE. As a complementing
result, it is shown that over structures with two total preorder relations as
well as over structures with one total preorder and two linear order relations,
the finite satisfiability problem for two-variable logic is undecidable
Reasoning about Data Repetitions with Counter Systems
We study linear-time temporal logics interpreted over data words with
multiple attributes. We restrict the atomic formulas to equalities of attribute
values in successive positions and to repetitions of attribute values in the
future or past. We demonstrate correspondences between satisfiability problems
for logics and reachability-like decision problems for counter systems. We show
that allowing/disallowing atomic formulas expressing repetitions of values in
the past corresponds to the reachability/coverability problem in Petri nets.
This gives us 2EXPSPACE upper bounds for several satisfiability problems. We
prove matching lower bounds by reduction from a reachability problem for a
newly introduced class of counter systems. This new class is a succinct version
of vector addition systems with states in which counters are accessed via
pointers, a potentially useful feature in other contexts. We strengthen further
the correspondences between data logics and counter systems by characterizing
the complexity of fragments, extensions and variants of the logic. For
instance, we precisely characterize the relationship between the number of
attributes allowed in the logic and the number of counters needed in the
counter system.Comment: 54 page
Path Checking for MTL and TPTL over Data Words
Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are
quantitative extensions of linear temporal logic, which are prominent and
widely used in the verification of real-timed systems. It was recently shown
that the path checking problem for MTL, when evaluated over finite timed words,
is in the parallel complexity class NC. In this paper, we derive precise
complexity results for the path-checking problem for MTL and TPTL when
evaluated over infinite data words over the non-negative integers. Such words
may be seen as the behaviours of one-counter machines. For this setting, we
give a complete analysis of the complexity of the path-checking problem
depending on the number of register variables and the encoding of constraint
numbers (unary or binary). As the two main results, we prove that the
path-checking problem for MTL is P-complete, whereas the path-checking problem
for TPTL is PSPACE-complete. The results yield the precise complexity of model
checking deterministic one-counter machines against formulae of MTL and TPTL
An automaton over data words that captures EMSO logic
We develop a general framework for the specification and implementation of
systems whose executions are words, or partial orders, over an infinite
alphabet. As a model of an implementation, we introduce class register
automata, a one-way automata model over words with multiple data values. Our
model combines register automata and class memory automata. It has natural
interpretations. In particular, it captures communicating automata with an
unbounded number of processes, whose semantics can be described as a set of
(dynamic) message sequence charts. On the specification side, we provide a
local existential monadic second-order logic that does not impose any
restriction on the number of variables. We study the realizability problem and
show that every formula from that logic can be effectively, and in elementary
time, translated into an equivalent class register automaton
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Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation
A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined
Finite Countermodel Based Verification for Program Transformation (A Case Study)
Both automatic program verification and program transformation are based on
program analysis. In the past decade a number of approaches using various
automatic general-purpose program transformation techniques (partial deduction,
specialization, supercompilation) for verification of unreachability properties
of computing systems were introduced and demonstrated. On the other hand, the
semantics based unfold-fold program transformation methods pose themselves
diverse kinds of reachability tasks and try to solve them, aiming at improving
the semantics tree of the program being transformed. That means some
general-purpose verification methods may be used for strengthening program
transformation techniques. This paper considers the question how finite
countermodels for safety verification method might be used in Turchin's
supercompilation method. We extract a number of supercompilation sub-algorithms
trying to solve reachability problems and demonstrate use of an external
countermodel finder for solving some of the problems.Comment: In Proceedings VPT 2015, arXiv:1512.0221
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