How unprovable is Rabin's decidability theorem?

We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical core of typical proofs of Rabin's theorem, is equivalent over the moderately strong second-order arithmetic theory $\mathsf{ACA}_0$ to a determinacy principle implied by the positional determinacy of all parity games and implying the determinacy of all Gale-Stewart games given by boolean combinations of ${\bf \Sigma^0_2}$ sets. It follows that complementation for tree automata is provable from $\Pi^1_3$- but not $\Delta^1_3$-comprehension. We then use results due to MedSalem-Tanaka, M\"ollerfeld and Heinatsch-M\"ollerfeld to prove that over $\Pi^1_2$-comprehension, the complementation theorem for tree automata, decidability of the MSO theory of the infinite binary tree, positional determinacy of parity games and determinacy of $\mathrm{Bool}({\bf \Sigma^0_2})$ Gale-Stewart games are all equivalent. Moreover, these statements are equivalent to the $\Pi^1_3$-reflection principle for $\Pi^1_2$-comprehension. It follows in particular that Rabin's decidability theorem is not provable in $\Delta^1_3$-comprehension.Comment: 21 page

Verifying Programs with Dynamic 1-Selector-Linked Structures in Regular Model Checking

International audienceWe address the problem of automatic verification of programs with dynamic data structures. We consider the case of sequential, non-recursive programs manipulating 1-selector-linked structures such as traditional linked lists (possibly sharing their tails) and circular lists. We propose an automata-based approach for a symbolic verification of such programs using the regular model checking framework. Given a program, the configurations of the memory are systematically encoded as words over a suitable finite alphabet, potentially infinite sets of configurations are represented by finite-state automata, and statements of the program are automatically translated into finite-state transducers defining regular relations between configurations. Then, abstract regular model checking techniques are applied in order to automatically check safety properties concerning the shape of the computed configurations or relating the input and output configurations. For that, we introduce new techniques for the computation of abstractions of the set of reachable configurations, and to refine these abstractions if spurious counterexamples are detected. Finally, we present experimental results showing the applicability of the approach and its efficiency

Sigref – A Symbolic Bisimulation Tool Box

We present a uniform signature-based approach to compute the most popular bisimulations. Our approach is implemented symbolically using BDDs, which enables the handling of very large transition systems. Signatures for the bisimulations are built up from a few generic building blocks, which naturally correspond to efficient BDD operations. Thus, the definition of an appropriate signature is the key for a rapid development of algorithms for other types of bisimulation. We provide experimental evidence of the viability of this approach by presenting computational results for many bisimulations on real-world instances. The experiments show cases where our framework can handle state spaces efficiently that are far too large to handle for any tool that requires an explicit state space description. This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS). See www.avacs.org for more information

A new low-field extremity magnetic resonance imaging and proposed compact MRI score: evaluation of anti-tumor necrosis factor biologics on rheumatoid arthritis

Magnetic resonance imaging (MRI) is a useful tool for evaluating disease activity and therapeutic efficacy in rheumatoid arthritis (RA). However, conventional whole-body MRI is inconvenient on several levels. We have therefore developed a new low-field extremity MRI (compact MRI, cMRI) and examined its clinical utility. Thirteen RA patients treated with anti-tumor necrosis factor (TNF) biologics were included in the study. The MRI was performed twice using a 0.21-T extremity MRI system. The MRI images were scored using our proposed cMRI scoring system, which we devised with reference to the Outcome Measures in Rheumatology Clinical Trials RA MRI score (OMERACT RAMRIS). In our cMRI scoring system, synovitis, bone edema, and bone erosion are separately graded on a scale from 0 to 3 by imaging over the whole hand, including the proximal interphalangeal joint. The total cMRI score (cMRIS) is then obtained by calculating the total bone erosion score × 1.5 + total bone edema score × 1.25 + total synovitis score. In this study, one patient showed a progression of bone destruction even under low clinical activity, as assessed by the disease activity score on 28 joints (DAS28); however, another patient’s cMRIS decreased concurrently with the decrease in DAS28, with the positive correlation observed between ΔDAS28 and ΔcMRIS (R = 0.055, P < 0.05). We conclude that cMRI and cMRIS are useful for assessing total disease activity and as a method linking MRI image evaluation to clinical evaluation

The Complexity of Nash Equilibria in Stochastic Multiplayer Games

We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a Nash equilibrium of G where Player 0 wins with probability 1? Moreover, this problem remains undecidable when restricted to pure strategies or (pure) strategies with finite memory. One way to obtain a decidable variant of the problem is to restrict the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively. Finally, we single out a special case of the general problem that, in many cases, admits an efficient solution. In particular, we prove that deciding the existence of an equilibrium in which each player either wins or loses with probability 1 can be done in polynomial time for games where the objective of each player is given by a parity condition with a bounded number of priorities

Canonical Graph Shapes

Abstract. Graphs are an intuitive model for states of a (software) system that include pointer structures — for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary in order to arrive at a tractable model. In this paper we propose a decidable fragment of first-order graph logic that we call local shape logic (LSL) as a possible abstraction mechanism, inspired by previous work of Sagiv, Reps and Wilhelm. An LSL formula constrains the multiplicities of nodes and edges in state graphs; abstraction is achieved by reasoning not about individual, concrete state graphs but about their characteristic shape properties. We go on to define the concept of the canonical shape of a state graph, which is expressed in a monomorphic sub-fragment of LSL, for which we define a graphical representation. We show that the canonical shapes give rise to an automatic finite abstraction of the state space of a software system, and we give an upper bound to the size of this abstract state space

ADP-Ribosylation Factor 6 Expression and Activation Are Reduced in Myometrium in Complicated Pregnancies

ARF6 (ADP-ribosylation factor 6) small GTP binding protein plays critical roles in actin cytoskeleton rearrangements and membrane trafficking, including internalisation of G protein coupled receptors (GPCR). ARF6 operates by cycling between GDP-bound (inactive) and GTP-bound (active) forms and is a potential regulator of GPCR-mediated uterine activity during pregnancy and labour. ARF6 contains very low intrinsic GTP binding activity and depends on GEFs (guanine nucleotide exchange factors) such as CYTH3 (cytohesin 3) to bind GTP. ARF6 and CYTH3 were originally cloned from human placenta, but there is no information on their expression in other reproductive tissues.The expression of ARF6, ARF1, and CYTH1-4 was investigated by measuring mRNA (using RT-PCR) and protein levels (using immunoblotting) in samples of myometrium obtained from non-pregnant women, and women with normal pregnancies, before or after the spontaneous onset of labour. We also analysed myometrial samples from women with spontaneous preterm labour and from women with complicated pregnancies requiring emergency preterm delivery. The GST)-effector pull down assay was used to study the presence of active ARF6 and ARF1 in all myometrial extracts.ARF6, ARF1 and CYTH3 but not CYTH1, CYTH2 and CYTH4 were expressed in all samples and the levels did not change with pregnancy or labour. However, ARF6 and CYTH3 but not ARF1 levels were significantly reduced in complicated pregnancies. The alterations in the expression of ARF6 and its GEF in human myometrium indicate a potential involvement of this signalling system in modulating the response of myometrial smooth muscle in complicated pregnancies. The levels of ARF6-GTP or ARF1-GTP did not change with pregnancy or labour but ARF6-GTP levels were significantly decreased in women with severe complications of pregnancy.We have demonstrated a functional ARF6 system in human myometrium and a correlation between ARF6 level and activity in uterine and abnormal pregnancy