108 research outputs found
Ordered Navigation on Multi-attributed Data Words
We study temporal logics and automata on multi-attributed data words.
Recently, BD-LTL was introduced as a temporal logic on data words extending LTL
by navigation along positions of single data values. As allowing for navigation
wrt. tuples of data values renders the logic undecidable, we introduce ND-LTL,
an extension of BD-LTL by a restricted form of tuple-navigation. While complete
ND-LTL is still undecidable, the two natural fragments allowing for either
future or past navigation along data values are shown to be Ackermann-hard, yet
decidability is obtained by reduction to nested multi-counter systems. To this
end, we introduce and study nested variants of data automata as an intermediate
model simplifying the constructions. To complement these results we show that
imposing the same restrictions on BD-LTL yields two 2ExpSpace-complete
fragments while satisfiability for the full logic is known to be as hard as
reachability in Petri nets
On the Path-Width of Integer Linear Programming
We consider the feasibility problem of integer linear programming (ILP). We
show that solutions of any ILP instance can be naturally represented by an
FO-definable class of graphs. For each solution there may be many graphs
representing it. However, one of these graphs is of path-width at most 2n,
where n is the number of variables in the instance. Since FO is decidable on
graphs of bounded path- width, we obtain an alternative decidability result for
ILP. The technique we use underlines a common principle to prove decidability
which has previously been employed for automata with auxiliary storage. We also
show how this new result links to automata theory and program verification.Comment: In Proceedings GandALF 2014, arXiv:1408.556
On Presburger arithmetic extended with non-unary counting quantifiers
We consider a first-order logic for the integers with addition. This logic
extends classical first-order logic by modulo-counting, threshold-counting, and
exact-counting quantifiers, all applied to tuples of variables. Further, the
residue in modulo-counting quantifiers is given as a term. Our main result
shows that satisfaction for this logic is decidable in two-fold exponential
space. If only threshold- and exact-counting quantifiers are allowed, we prove
an upper bound of alternating two-fold exponential time with linearly many
alternations. This latter result almost matches Berman's exact complexity of
first-order logic without counting quantifiers.
To obtain these results, we first translate threshold- and exact-counting
quantifiers into classical first-order logic in polynomial time (which already
proves the second result). To handle the remaining modulo-counting quantifiers
for tuples, we first reduce them in doubly exponential time to modulo-counting
quantifiers for single elements. For these quantifiers, we provide a quantifier
elimination procedure similar to Reddy and Loveland's procedure for first-order
logic and analyse the growth of coefficients, constants, and moduli appearing
in this process. The bounds obtained this way allow to replace quantification
in the original formula to integers of bounded size which then implies the
first result mentioned above.
Our logic is incomparable with the logic considered recently by Chistikov et
al. They allow more general counting operations in quantifiers, but only unary
quantifiers. The move from unary to non-unary quantifiers is non-trivial,
since, e.g., the non-unary version of the H\"artig quantifier results in an
undecidable theory
Ehrenfeucht-Fraïssé goes elementarily automatic for structures of bounded degree
International audienceMany relational structures are automatically presentable, i.e. elements of the domain can be seen as words over a finite alphabet and equality and other atomic relations are represented with finite automata. The first-order theories over such structures are known to be primitive recursive, which is shown by the inductive construction of an automaton representing any relation definable in the first-order logic. We propose a general method based on Ehrenfeucht-Fraïssé games to give upper bounds on the size of these automata and on the time required to build them. We apply this method for two different automatic structures which have elementary decision procedures, Presburger Arithmetic and automatic structures of bounded degree. For the latter no upper bound on the size of the automata was known. We conclude that the very general and simple automata-based algorithm works well to decide the first-order theories over these structures
Abstract Regular Tree Model Checking
International audienceRegular (tree) model checking (RMC) is a promising generic method for formal verification of infinite-state systems. It encodes configurations of systems as words or trees over a suitable alphabet, possibly infinite sets of configurations as finite word or tree automata, and operations of the systems being examined as finite word or tree transducers. The reachability set is then computed by a repeated application of the transducers on the automata representing the currently known set of reachable configurations. In order to facilitate termination of RMC, various acceleration schemas have been proposed. One of them is a combination of RMC with the abstract-check-refine paradigm yielding the so-called abstract regular model checking (ARMC). ARMC has originally been proposed for word automata and transducers only and thus for dealing with systems with linear (or easily linearisable) structure. In this paper, we propose a generalisation of ARMC to the case of dealing with trees which arise naturally in a lot of modelling and verification contexts. In particular, we first propose abstractions of tree automata based on collapsing their states having an equal language of trees up to some bounded height. Then, we propose an abstraction based on collapsing states having a non-empty intersection (and thus "satisfying") the same bottom-up tree "predicate" languages. Finally, we show on several examples that the methods we propose give us very encouraging verification results
A Robust Class of Data Languages and an Application to Learning
We introduce session automata, an automata model to process data words, i.e.,
words over an infinite alphabet. Session automata support the notion of fresh
data values, which are well suited for modeling protocols in which sessions
using fresh values are of major interest, like in security protocols or ad-hoc
networks. Session automata have an expressiveness partly extending, partly
reducing that of classical register automata. We show that, unlike register
automata and their various extensions, session automata are robust: They (i)
are closed under intersection, union, and (resource-sensitive) complementation,
(ii) admit a symbolic regular representation, (iii) have a decidable inclusion
problem (unlike register automata), and (iv) enjoy logical characterizations.
Using these results, we establish a learning algorithm to infer session
automata through membership and equivalence queries
Model-Checking Counting Temporal Logics on Flat Structures
We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold. For most of these extensions, the model-checking problem is undecidable, but we show that decidability can be recovered by considering flat Kripke structures where each state belongs to at most one simple loop. Most decision procedures are based on results on (flat) counter systems where counters are used to implement the evaluation of counting operators
Neoadjuvant chemoradiation with Gemcitabine for locally advanced pancreatic cancer
<p>Abstract</p> <p>Introduction</p> <p>To evaluate efficacy and secondary resectability in patients with locally advanced pancreatic cancer (LAPC) treated with neoadjuvant chemoradiotherapy (CRT).</p> <p>Patients and methods</p> <p>A total of 215 patients with locally advanced pancreatic cancer were treated with chemoradiation at a single institution. Radiotherapy was delivered with a median dose of 52.2 Gy in single fractions of 1.8 Gy. Chemotherapy was applied concomitantly as gemcitabine (GEM) at a dose of 300 mg/m<sup>2 </sup>weekly, followed by adjuvant cycles of full-dose GEM (1000 mg/m<sup>2</sup>). After neoadjuvant CRT restaging was done to evaluate secondary resectability. Overall and disease-free survival were calculated and prognostic factors were estimated.</p> <p>Results</p> <p>After CRT a total of 26% of all patients with primary unresectable LAPC were chosen to undergo secondary resection. Tumour free resection margins could be achieved in 39.2% (R0-resection), R1-resections were seen in 41.2%, residual macroscopic tumour in 11.8% (R2) and in 7.8% resection were classified as Rx. Patients with complete resection after CRT showed a significantly increased median overall survival (OS) with 22.1 compared to 11.9 months in non-resected patients. Median OS and disease-free survival (DFS) of all patients were 12.3 and 8.1 months respectively. In most cases the first site of disease progression was systemic with hepatic (52%) and peritoneal (36%) metastases.</p> <p>Discussion</p> <p>A high percentage of patients with locally advanced pancreatic cancer can undergo secondary resection after gemcitabine-based chemoradiation and has a relative long-term prognosis after complete resection.</p
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