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We present a formal methodology and tool for uncovering errors in the interaction of software modules. Our methodology consists of a suite of languages for defining software interfaces, and algorithms for checking interface compatibility. We focus on interfaces that explain the method-call dependencies between software modules. Such an interface makes assumptions about the environment in the form of call and availability constraints. A call constraint restricts the accessibility of local methods to certain external methods. An availability constraint restricts the accessibility of local methods to certain states of the module. For example, the interface for a file server with local methods open and read may assert that a file cannot be read without having been opened. Checking interface compatibility requires the solution of games, and in the presence of availability constraints, of pushdown games. Based on this methodology, we have implemented a tool that has uncovered incompatibilities in TinyOS, a small operating system for sensor nodes in adhoc networks.

Abstract. We define and study a quantitative generalization of the traditional boolean framework of model-based specification and verification. In our setting, propositions have integer values at states, and properties have integer values on traces. For example, the value of a quantitative proposition at a state may represent power consumed at the state, and the value of a quantitative property on a trace may represent energy used along the trace. The value of a quantitative property at a state, then, is the maximum (or minimum) value achievable over all possible traces from the state. In this framework, model checking can be used to compute, for example, the minimum battery capacity necessary for achieving a given objective, or the maximal achievable lifetime of a system with a given initial battery capacity. In the case of open systems, these problems require the solution of games with integer values.Quantitative model checking and game solving is undecidable, except if bounds on the computation can be found. Indeed, many interesting quantitative properties, like minimal necessary battery capacity and maximal achievable lifetime, can be naturally specified by quantitativebound automata, which are finite automata with integer registers whose analysis is constrained by a bound function f that maps each system K to an integer f (K). Along with the linear-time, automaton-based view of quantitative verification, we present a corresponding branching-time view based on a quantitative-bound µ-calculus, and we study the relationship, expressive power, and complexity of both views.

Sedimentary structures of some coastal tropical tidal flats of the east coast of India, and inner estuarine tidal point bars located at 30 to 50 kilometers inland from the coast, have been extensively studied under varying seasonal conditions. The results reveal that physical features such as flaser bedding, herringbone cross-bedding, lenticular bedding, and mud/silt couplets are common to both the environments. In fact, flaser bedding and lenticular bedding are more common in the point bar facies during the monsoon months than in the coastal tidal flat environments. Interference ripples, though common in both the environments, show different architectural patterns for different environmental domains. Interference ripples with thread-like secondary set overriding the earlier ripple-form, resembling wrinkle marks, are the typical features in estuarine point bars near the high water region. Because structures which are so far considered as key structures for near-coastal tidal flats are common to both the environments, caution should be exercised for deciphering palaeo-environments, particularly for Proterozoic rocks, where one has to depend only on physical sedimentary structures.

The composition of sandstones often provides key evidence about the tectonic, weathering and transport processes operating on the surface at the time of deposition. Petrologic and geochemical analyses of little-metamorphosed middle^late Archean sandstones from the Eastern Indian Craton show that the sedimentary rocks were derived from dominantly 3.3-Ga-old amphibolites of the Older Metamorphic Group (OMG) and tonalites of the Older Metamorphic Tonalite Gneisses (OMTG), the two oldest lithologic units of this craton. Chondrite-normalized rare earth element (REE) patterns of the sandstones show a light REE-enriched signature with (La/Sm) N varying from 5.2 to 6.7 with no Eu anomaly, while the heavy REEs display flat patterns with (Gd/Lu) N values of 0.9^1.6. Primitive mantle-normalized incompatible and compatible trace element plots of these sandstones demonstrate an overall similarity with global Proterozoic^Archean sandstones, including strong Nb^Ta negative anomalies. In an f Sm=Nd vs. O Nd (0) diagram, the sandstones plot precisely between the regional amphibolites and tonalites. We infer from the REE abundances and the f Sm=Nd vs. O Nd (0) plot that the sandstones represent a bimodal mechanical mixture of OMG and OMTG. The low Ce/Pb ratios of these rocks of 1^4 indicate a variably Pb-enriched Archean crust and that the Ce/Pb ratio acquired the continental crustal signature, distinctly different from those of the bulk silicate earth and mantle values at least as early as mid-Archean. Strong Nb^Ta depletion relative to the primitive mantle suggests the sandstones were derived from subduction-related magmatic arc sources. This latter suggestion is strongly supported by the low Nb/Ta and high Zr/Sm ratios of these sandstones, identical to Archean tonalite^trondhjemites that require, based on recent trace-element partitioning results, their protoliths to have formed by subduction melting of lowmagnesium amphibolites or metamorphosed hydrous basalts [1,2]. The average Nd model ages of the sandstones are greater than the Sm^Nd crystallization ages of the OMG and OMTG at V3.3 Ga. The geochemical data presented here can be collectively interpreted to suggest the presence of subduction^accretion processes operational in the midArchean Eastern Indian Craton. Because the OMG and OMTG, the source rocks of the sandstones, formed in a subduction-related arc setting, the basement rocks upon which this arc was constructed must have been older. This observation and the depleted mantle Nd model ages (T DM ) of the sandstones, ranging from 3.6 to 4.0 Ga, strongly indicate the presence of continental crust in this Eastern Indian craton older than 3.3 Ga and possibly as old as 0012-821X / 04 / $^see front matter ß