On the equivalence of game and denotational semantics for the probabilistic mu-calculus

The probabilistic (or quantitative) modal mu-calculus is a fixed-point logic de- signed for expressing properties of probabilistic labeled transition systems (PLTS). Two semantics have been studied for this logic, both assigning to every process state a value in the interval [0,1] representing the probability that the property expressed by the formula holds at the state. One semantics is denotational and the other is a game semantics, specified in terms of two-player stochastic games. The two semantics have been proved to coincide on all finite PLTS's, but the equivalence of the two semantics on arbitrary models has been open in literature. In this paper we prove that the equivalence indeed holds for arbitrary infinite models, and thus our result strengthens the fruitful connection between denotational and game semantics. Our proof adapts the unraveling or unfolding method, a general proof technique for proving result of parity games by induction on their complexity

On the Proof Theory of Regular Fixed Points

International audienceWe consider encoding finite automata as least fixed points in a proof theoretical framework equipped with a general induction scheme, and study automata inclusion in that setting. We provide a coinductive characterization of inclusion that yields a natural bridge to proof-theory. This leads us to generalize these observations to regular formulas, obtaining new insights about inductive theorem proving and cyclic proofs in particular

Infinets: The parallel syntax for non-wellfounded proof-theory

Logics based on the µ-calculus are used to model induc-tive and coinductive reasoning and to verify reactive systems. A well-structured proof-theory is needed in order to apply such logics to the study of programming languages with (co)inductive data types and automated (co)inductive theorem proving. While traditional proof system suffers some defects, non-wellfounded (or infinitary) and circular proofs have been recognized as a valuable alternative, and significant progress have been made in this direction in recent years. Such proofs are non-wellfounded sequent derivations together with a global validity condition expressed in terms of progressing threads. The present paper investigates a discrepancy found in such proof systems , between the sequential nature of sequent proofs and the parallel structure of threads: various proof attempts may have the exact threading structure while differing in the order of inference rules applications. The paper introduces infinets, that are proof-nets for non-wellfounded proofs in the setting of multiplicative linear logic with least and greatest fixed-points (µMLL ∞) and study their correctness and sequentialization. Inductive and coinductive reasoning is pervasive in computer science to specify and reason about infinite data as well as reactive properties. Developing appropriate proof systems amenable to automated reasoning over (co)inductive statements is therefore important for designing programs as well as for analyzing computational systems. Various logical settings have been introduced to reason about such inductive and coinductive statements, both at the level of the logical languages modelling (co)induction (such as Martin Löf's inductive predicates or fixed-point logics, also known as µ-calculi) and at the level of the proof-theoretical framework considered (finite proofs with explicit (co)induction rulesà la Park [23] or infinite, non-wellfounded proofs with fixed-point unfold-ings) [6-8, 4, 1, 2]. Moreover, such proof systems have been considered over classical logic [6, 8], intuitionistic logic [9], linear-time or branching-time temporal logic [19, 18, 25, 26, 13-15] or linear logic [24, 16, 4, 3, 14]

Cryo-EM structure of a helicase loading intermediate containing ORC-Cdc6-Cdt1-MCM2-7 bound to DNA

In eukaryotes, the Cdt1-bound replicative helicase core MCM2-7 is loaded onto DNA by the ORC-Cdc6 ATPase to form a prereplicative complex (pre-RC) with an MCM2-7 double hexamer encircling DNA. Using purified components in the presence of ATP-γS, we have captured in vitro an intermediate in pre-RC assembly that contains a complex between the ORC-Cdc6 and Cdt1-MCM2-7 heteroheptamers called the OCCM. Cryo-EM studies of this 14-subunit complex reveal that the two separate heptameric complexes are engaged extensively, with the ORC-Cdc6 N-terminal AAA+ domains latching onto the C-terminal AAA+ motor domains of the MCM2-7 hexamer. The conformation of ORC-Cdc6 undergoes a concerted change into a right-handed spiral with helical symmetry that is identical to that of the DNA double helix. The resulting ORC-Cdc6 helicase loader shows a notable structural similarity to the replication factor C clamp loader, suggesting a conserved mechanism of action

The Involutive Quantaloid of Completely Distributive Lattices

Let L be a complete lattice and let Q(L) be the unital quantale of join-continuous endo-functions of L. We prove the following result: Q(L) is an involutive (that is, non-commutative cyclic ⋆-autonomous) quantale if and only if L is a completely distributive lattice. If this is the case, then the dual tensor operation corresponds, via Raney's transforms, to composition in the (dual) quantale of meet-continuous endo-functions of L. Let sLatt be the category of sup-lattices and join-continuous functions and let cdLatt be the full subcategory of sLatt whose objects are the completely distributive lattices. We argue that (i) cdLatt is itself an involutive quantaloid, and therefore it is the largest full-subcategory of sLatt with this property; (ii) cdLatt is closed under the monoidal operations of sLatt and, consequently, if Q(L) is involutive, then Q(L) is completely distributive as well

Automatic cyclic termination proofs for recursive procedures in separation logic

We describe a formal verification framework and tool implementation, based upon cyclic proofs, for certifying the safe termination of imperative pointer programs with recursive procedures. Our assertions are symbolic heaps in separation logic with user defined inductive predicates; we employ explicit approximations of these predicates as our termination measures. This enables us to extend cyclic proof to programs with procedures by relating these measures across the pre- and postconditions of procedure calls. We provide an implementation of our formal proof system in the Cyclist theorem proving framework, and evaluate its performance on a range of examples drawn from the literature on program termination. Our implementation extends the current state-of-the-art in cyclic proof-based program verification, enabling automatic termination proofs of a larger set of programs than previously possible

Replication fork stalling by bulky DNA damage: localization at active origins and checkpoint modulation

The integrity of the genome is threatened by DNA damage that blocks the progression of replication forks. Little is known about the genomic locations of replication fork stalling, and its determinants and consequences in vivo. Here we show that bulky DNA damaging agents induce localized fork stalling at yeast replication origins, and that localized stalling is dependent on proximal origin activity and is modulated by the intra–S–phase checkpoint. Fork stalling preceded the formation of sister chromatid junctions required for bypassing DNA damage. Despite DNA adduct formation, localized fork stalling was abrogated at an origin inactivated by a point mutation and prominent stalling was not detected at naturally-inactive origins in the replicon. The intra–S–phase checkpoint contributed to the high-level of fork stalling at early origins, while checkpoint inactivation led to initiation, localized stalling and chromatid joining at a late origin. Our results indicate that replication forks initially encountering a bulky DNA adduct exhibit a dual nature of stalling: a checkpoint-independent arrest that triggers sister chromatid junction formation, as well as a checkpoint-enhanced arrest at early origins that accompanies the repression of late origin firing. We propose that the initial checkpoint-enhanced arrest reflects events that facilitate fork resolution at subsequent lesions

Global Profiling of DNA Replication Timing and Efficiency Reveals that Efficient Replication/Firing Occurs Late during S-Phase in S. pombe

10.1371/journal.pone.0000722PLoS ONE2

Nuclear Mitochondrial DNA Activates Replication in Saccharomyces cerevisiae

The nuclear genome of eukaryotes is colonized by DNA fragments of mitochondrial origin, called NUMTs. These insertions have been associated with a variety of germ-line diseases in humans. The significance of this uptake of potentially dangerous sequences into the nuclear genome is unclear. Here we provide functional evidence that sequences of mitochondrial origin promote nuclear DNA replication in Saccharomyces cerevisiae. We show that NUMTs are rich in key autonomously replicating sequence (ARS) consensus motifs, whose mutation results in the reduction or loss of DNA replication activity. Furthermore, 2D-gel analysis of the mrc1 mutant exposed to hydroxyurea shows that several NUMTs function as late chromosomal origins. We also show that NUMTs located close to or within ARS provide key sequence elements for replication. Thus NUMTs can act as independent origins, when inserted in an appropriate genomic context or affect the efficiency of pre-existing origins. These findings show that migratory mitochondrial DNAs can impact on the replication of the nuclear region they are inserted in

ATP-dependent chromatin remodeling shapes the DNA replication landscape.

The eukaryotic DNA replication machinery must traverse every nucleosome in the genome during S phase. As nucleosomes are generally inhibitory to DNA-dependent processes, chromatin structure must undergo extensive reorganization to facilitate DNA synthesis. However, the identity of chromatin-remodeling factors involved in replication and how they affect DNA synthesis is largely unknown. Here we show that two highly conserved ATP-dependent chromatin-remodeling complexes in Saccharomyces cerevisiae, Isw2 and Ino80, function in parallel to promote replication fork progression. As a result, Isw2 and Ino80 have especially important roles for replication of late-replicating regions during periods of replication stress. Both Isw2 and Ino80 complexes are enriched at sites of replication, suggesting that these complexes act directly to promote fork progression. These findings identify ATP-dependent chromatin-remodeling complexes that promote DNA replication and define a specific stage of replication that requires remodeling for normal function