Abstract:
A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. Safety one-way alternating automata with one register on infinite data words are considered, their nonemptiness is shown EXPSPACE-complete, and their inclusion decidable but not primitive recursive. The same complexity bounds are obtained for satisfiability and refinement, respectively, for the safety fragment of linear temporal logic with freeze quantification. Dropping the safety restriction, adding past temporal operators, or adding one more register, each causes undecidability.

Abstract:
By adapting the iterative yardstick construction of Stockmeyer, we show that the reachability problem for vector addition systems with a stack does not have elementary complexity. As a corollary, the same lower bound holds for the satisfiability problem for a two-variable first-order logic on trees in which unbounded data may label only leaf nodes. Whether the two problems are decidable remains an open question.

Abstract:
A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. To reason about data words, linear temporal logic is extended by the freeze quantifier, which stores the element at the current word position into a register, for equality comparisons deeper in the formula. By translations from the logic to alternating automata with registers and then to faulty counter automata whose counters may erroneously increase at any time, and from faulty and error-free counter automata to the logic, we obtain a complete complexity table for logical fragments defined by varying the set of temporal operators and the number of registers. In particular, the logic with future-time operators and 1 register is decidable but not primitive recursive over finite data words. Adding past-time operators or 1 more register, or switching to infinite data words, cause undecidability.

Abstract:
A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element ("datum") from an infinite set, where the latter can only be compared for equality. The article considers alternating automata on data trees that can move downward and rightward, and have one register for storing data. The main results are that nonemptiness over finite data trees is decidable but not primitive recursive, and that nonemptiness of safety automata is decidable but not elementary. The proofs use nondeterministic tree automata with faulty counters. Allowing upward moves, leftward moves, or two registers, each causes undecidability. As corollaries, decidability is obtained for two data-sensitive fragments of the XPath query language.

Abstract:
Constraint LTL, a generalisation of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some real-time logics, but this variable-binding mechanism is quite general and ubiquitous in many logical languages (first-order temporal logics, hybrid logics, logics for sequence diagrams, navigation logics, logics with lambda-abstraction etc.). We show that Constraint LTL over the simple domain (N,=) augmented with the freeze quantifier is undecidable which is a surprising result in view of the poor language for constraints (only equality tests). Many versions of freeze-free Constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes Sigma_1^1-completeness. On the positive side, we provide complexity results when the domain is finite (EXPSPACE-completeness) or when the formulae are flat in a sense introduced in the paper. Our undecidability results are sharp (i.e. with restrictions on the number of variables) and all our complexity characterisations ensure completeness with respect to some complexity class (mainly PSPACE and EXPSPACE).

Abstract:
We study complexity of the model-checking problems for LTL with registers (also known as freeze LTL) and for first-order logic with data equality tests over one-counter automata. We consider several classes of one-counter automata (mainly deterministic vs. nondeterministic) and several logical fragments (restriction on the number of registers or variables and on the use of propositional variables for control locations). The logics have the ability to store a counter value and to test it later against the current counter value. We show that model checking over deterministic one-counter automata is PSPACE-complete with infinite and finite accepting runs. By constrast, we prove that model checking freeze LTL in which the until operator is restricted to the eventually operator over nondeterministic one-counter automata is undecidable even if only one register is used and with no propositional variable. As a corollary of our proof, this also holds for first-order logic with data equality tests restricted to two variables. This makes a difference with the facts that several verification problems for one-counter automata are known to be decidable with relatively low complexity, and that finitary satisfiability for the two logics are decidable. Our results pave the way for model-checking memoryful (linear-time) logics over other classes of operational models, such as reversal-bounded counter machines.

Abstract:
We analysed the collection of available protein trap lines in Drosophila melanogaster and identified potential biases that are likely to restrict genome coverage in protein trap screens. The protein trap screens investigated here primarily used P-element vectors and thus exhibit some of the same positional biases associated with this transposon that are evident from the comprehensive Drosophila Gene Disruption Project. We further found that protein trap target genes usually exhibit broad and persistent expression during embryonic development, which is likely to facilitate better detection. In addition, we investigated the likely influence of the GFP exon on host protein structure and found that protein trap insertions have a significant bias for exon-exon boundaries that encode disordered protein regions. 38.8% of GFP insertions land in disordered protein regions compared with only 23.4% in the case of non-trapping P-element insertions landing in coding sequence introns (p < 10-4). Interestingly, even in cases where protein domains are predicted, protein trap insertions frequently occur in regions encoding surface exposed areas that are likely to be functionally neutral. Considering the various biases observed, we predict that less than one third of intron-containing genes are likely to be amenable to trapping by the existing methods.Our analyses suggest that the utility of P-element vectors for protein trap screens has largely been exhausted, and that approximately 2,800 genes may still be amenable using piggyBac vectors. Thus protein trap strategies based on current approaches are unlikely to offer true genome-wide coverage. We suggest that either transposons with reduced insertion bias or recombineering-based targeting techniques will be required for comprehensive genome coverage in Drosophila.Genetic trapping experiments have a long-standing history in Drosophila functional genomics. The classic "enhancer trap" screens utilised P-element-mediated insertion of th

Abstract:
The purpose of this paper is to lay the foundations for the theory of higher rank b-divisorial algebras of Shokurov type. We develop techniques to deal with such objects and propose two natural conjectures regarding Shokurov algebras and adjoint algebras. We confirm these conjectures in the case of affine curves.