Modelling coalitions: ATL + argumentation

In this thesis, we introduce and examine four new temporal logic formalisms that can be used as specification languages for the automated verification of the reliability of hardware and software designs with respect to a desired behavior. The work is organized in two parts. In the first one, we reason about two logics for computations, GCTL* and MCTL*, which are useful to describe a correct execution of monolithic closed systems. In the second one, instead, we focus on two logics for strategies, SL and mATL*, which are useful to formalize several interesting properties about interactive plays in multi-entities systems modeled as multi-agent games. In the “Logics for Computations” part, we first study the immersion of the idea of graded quantifications into the temporal-logic framework. In first order logic, existential and universal quantifiers express the concepts of the existence of at least one individual object satisfying a formula, or that all individual objects satisfy a formula. In other logics, these quantifiers have been generalized to express that, for a given non-negative integer n, at least n or all but n individuals satisfy a particular formula. Here, we consider GCTL, a temporal logic with graded path quantifiers, which allows to describe properties like “there exist at least n different classes of computational fluxes in which a system reaches a predetermined state”, where the classes over paths are computed by means of a predetermined equivalence relation. More precisely, we uniformly extend the classic concept of graded quantifiers from states to paths, through the use of a concept of path equivalence with respect to a given path formula. About this logic, in particular, we study the expressiveness and succinctness relationships with respect to GµCalculus and the complexity of the satisfiability problem, which results to be ExpTime-Complete. This research is partially based on the works [BMM09] “Graded Computation Tree Logic” and [BMM10] “Graded Computation Tree Logic with Binary Coding” published, respectively, in the proceedings of the “IEEE Symposium on Logic in Computer Science, 2009” and “EACSL Annual Conference on Computer Science Logic, 2010”. Preliminary results can be also found in [Mog07]. Furthermore, we consider special quantifiers over substructures, which allow to select, using parametric criteria, small critical parts of a system to be successively verified. In literature, there are some attempts to define a logic that allows to modify the underlying structure under exam and then to verify on it some assigned property. However, as far as we know, none of them is able to select minimal submodels of a given property describing the criteria on which then execute the verification process. Here, we base our work on the search of a new operator that merges the concept of quantifiers on structures with that one derived by a generalization of the concept of pruning. The results of this work, is a class of three different extensions of CTL* with minimal model quantifiers, which we name MCTL*. Regarding these logics, we study several reductions among them, as well as the satisfiability problem that we prove to be highly undecidability, i.e., Σ_1^1-Hard, for two out of the three cases. This research is partially based on the work [MM09] “Branching-Time Temporal Logics with Minimal Model Quantifiers” published in the proceedings of the “International Conference on Developments in Language Theory, 2009”. In the “Logics for Strategies” part, we first study the problem of defining a new specification language through which it is possible to express several important properties of multi-entities systems that are neither expressible using classical monolithic temporal logics, such as CTL*, nor using two-agent-teams temporal logics, such as ATL*. In literature, we can found some proposal of logics that try to achieve this goal, but unfortunately, none of them succeeds completely on all the aspects. Among them, one of the most important attempts is CHP-SL, a logics in which one can use variables over strategies. However, this logic has a deep weakness, since it does not allow to describe games with more than two players and even two-players concurrent games. Here, we introduce SL, a logic with a syntax similar in some aspects to the first order logic, in which the strategies of the agent building the game are treated as first order objects on which we can quantify. This logic generalizes CHP-SL, by allowing the specification of the correct behavior of multi-agent concurrent games. In SL, for example, we are able to express very complex but useful Nash equilibria that are not expressible with CHP-SL. We enlighten that Nash equilibrium is one of the most important concepts in game theory. For the introduced logic, we solve two problems left open in the work on CHP-SL. Precisely, we show that the related model-checking problem is 2ExpTime-Complete, thus not harder of the same problem for several subsumed logics, while we prove that its satisfiability problem is highly undecidable, i.e., Σ_1^1-Hard. This research is partially based on the work [MMV10a] “Reasoning About Strategies” published in the proceedings of the “IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, 2010”. Finally, we consider the concept of relentful strategic reasoning, i.e., a formalism that expresses the ability of a strategy to be used not only to achieve a first given goal, but also to change its final goal in dependence of the history of the play. In the context of planning, memoryful quantification, i.e., quantification over computations that does not lose information about the past along the time, is one of the principal way to express the fact that a system is able to achieve a desired result, and shift to a different goal if some event happens. However, this kind of quantification was not considered before in the context of multi-agent planning. Here, we introduce mATL*, a fusion of the classic alternating temporal logic ATL* with memoryful quantification, with the aim of covering the previous idea. About this logics, we prove that, although it is equivalent to ATL*, it is exponentially more succinct. Nevertheless, we prove that both the model-checking and the satisfiability problems remain 2ExpTime-Complete, as for ATL*. This research is partially based on the work [MMV10b] “Relentful Strategic Reasoning in Alternating-Time Temporal Logic” published in the proceedings of the “International Conference on Logic for Programming Artificial Intelligence and Reasoning, 2010”.

Many problems in AI and multi-agent systems research are most naturally formulated in terms of the abilities of a coalition of agents. There exist several excellent logical tools for reasoning about coalitional ability. However, coalitional ability can be affected by the availability of resources, and there is no straightforward way of reasoning about resource requirements in logics such as Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). In this paper, we propose a logic for reasoning about coalitional ability under resource constraints. We extend ATL with costs of actions and hence of strategies. We give a complete and sound axiomatisation of the resulting logic Resource-Bounded ATL (RB-ATL) and an efficient model-checking algorithm for it.

In the last few years, argumentation frameworks have been successfully applied to multi agent systems. Recently, argumentation has been used to provide a framework for reasoning about coalition formation. At the same time alternating-time temporal logic has been used to reason about the behavior and abilities of coalitions of agents. However, ATL operators account only for the existence of successful strategies of coalitions. They do not consider whether coalitions can be actually formed. This paper is an attempt to combine both frameworks and to develop a logic through which we can reason at the same time (1) about abilities of coalitions of agents and (2) about the formation of coalitions. We provide a formal extension of ATL, ATLc, in which the actual computation of the coalition is modelled in terms of argumentation semantics. We show that ATLc's proof theory can be understood as a natural extension of the model checking procedure used in ATL.

Different agents may have different points of view. This can be modelled using different abstract argumentation frameworks, each consisting of a set of arguments and a binary attack-relation between them. A question arising in this context is whether the diversity of views observed in such a profile of argumentation frameworks is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual attack-relation between the arguments and, second, the personal preferences of the agent concerned. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. This is useful for understanding what types of profiles can reasonably be expected to come up in a multiagent system.

We address the problem of learning temporal properties from the branching-time behavior of systems. Existing research in this field has mostly focused on learning linear temporal properties specified using popular logics, such as Linear Temporal Logic (LTL) and Signal Temporal Logic (STL). Branching-time logics such as Computation Tree Logic (CTL) and Alternating-time Temporal Logic (ATL), despite being extensively used in specifying and verifying distributed and multi-agent systems, have not received adequate attention. Thus, in this paper, we investigate the problem of learning CTL and ATL formulas from examples of system behavior. As input to the learning problems, we rely on the typical representations of branching behavior as Kripke structures and concurrent game structures, respectively. Given a sample of structures, we learn concise formulas by encoding the learning problem into a satisfiability problem, most notably by symbolically encoding both the search for prospective formulas and their fixed-point based model checking algorithms. We also study the decision problem of checking the existence of prospective ATL formulas for a given sample. We implement our algorithms in a Python prototype and have evaluated them to extract several common CTL and ATL formulas used in practical applications.

Alternating-time temporal logic (atl) is a logic for reasoning about open computational systems and multi-agent systems. It is well known that atl model checking is linear in the size of the model. We point out, however, that the size of an atl model is usually exponential in the number of agents. When the size of models is defined in terms of states and agents rather than transitions, it turns out that the problem is (1) Δ3P-complete for concurrent game structures, and (2) Δ2P-complete for alternating transition systems. Moreover, for “Positive atl” that allows for negation only on the level of propositions, model checking is (1) Σ2P-complete for concurrent game structures, and (2) NP-complete for alternating transition systems. We show a nondeterministic polynomial reduction from checking arbitrary alternating transition systems to checking turn-based transition systems, We also discuss the determinism assumption in alternating transition systems, and show that it can be easily removed. In the second part of the paper, we study the model checking complexity for formulae of atlwith imperfect information (atlir). We show that the problem is Δ2P-complete in the number of transitions and the length of the formula (thereby closing a gap in previous work of Schobbens in Electron. Notes Theor. Comput. Sci. 85(2), 2004). Then, we take a closer look and use the same fine structure complexity measure as we did for atl with perfect information. We get the surprising result that checking formulae of atlir is also Δ3P-complete in the general case, and Σ2P-complete for “Positive atlir”. Thus, model checking agents’ abilities for both perfect and imperfect information systems belongs to the same complexity class when a finer-grained analysis is used.

An exploration into the assessment of hip extension strength and its importance for performance in professional soccer.

Syntax and semantics are proposed for realtime (i.e., continuous-time) regular expressions, which extend and generalize existing SVA regular expressions. The extensions are motivated by practical needs for AMS circuit verification and were developed as part of the authors' contribution to analog assertions work in the Accellera committee standardizing Verilog-AMS. Given a suitable notion of sampling, we prove that the realtime semantics provided for the existing SVA clocked digital regular expressions is equivalent to the original discrete semantics. As a result, the existing digital operators can intermix freely with the new realtime operators, which is a major contribution of our framework. We also investigate the theoretical relationship between our framework and the timed regular expressions of Asarin, Caspi, and Maler. We provide a semantically faithful embedding of timed regular expressions into our realtime regular expressions, as well as a construction of timed automata recognizers for our realtime regular expressions. These constructions show that our realtime regular expressions are no less expressive than the timed regular expressions of [1] and no more expressive than the generalized timed regular expressions of [2]. The automata recognizers also provide the basis for an implementation strategy for our framework.

Cluster computing has recently gone through an evolution from single processor systems to multicore/multi-socket systems. This has resulted in lowering the cost/performance ratio of the compute machines. Compute farms that host these machines tend to become heterogeneous over time due to incremental extensions, hardware upgrades and/or nodes being purchased for users with particular needs. This heterogeneity is not surprising given the wide range of processor, memory and network technologies that become available and the relatively small price difference between these various options. Different CPU architectures, memory capacities, communication and I/O interfaces of the participating compute nodes present many challenges to job scheduling and often result in under or over utilization of the compute resources. In general, it is not feasible for the application programmers to specifically optimize their programs for such a set of differing compute nodes, due to the difficulty and time-intensiveness of such a task. The trend of heterogeneous compute farms has coincided with resurgence in the virtualization technology. Virtualization technology is receiving widespread adoption, mainly due to the benefits of server consolidation and isolation, load balancing, security and fault tolerance. Virtualization has also generated considerable interest in the High Performance Computing (HPC) community, due to the resulting high availability, fault tolerance, cluster partitioning and accommodation of conflicting user requirements. However, the HPC community is still wary of the potential overheads associated with virtualization, as it results in slower network communications and disk I/O, which need to be addressed. The live migration feature, available to most virtualization technologies, can be leveraged to improve the throughput of a heterogeneous compute farm (HC) used for HPC applications. For this we mitigated the slow network communication in Xen; an open source virtual machine monitor. We present a detailed analysis of the communication framework of Xen and propose communication configurations that give 50% improvement over the conventional Xen network configuration. From a detailed study of the migration facility in Xen, we propose an improvement in the live migration facility specifically targeting HPC applications. This optimization gives around 50% improvement over the default migration facility of Xen. In this thesis, we also investigate resource scheduling in heterogeneous compute farm with the perspective of dynamic resource re-mapping. Our approach is to profile each job in the compute farm at runtime, and propose a better resource mapping compared to the initial allocation. We then migrate the job(s) to the best-suited homogeneous sub-cluster to improve overall throughput of the HC. For this, we develop a novel heterogeneity and virtualization-aware profiling framework, which is able to predict the CPU and communication characteristics of high performance scientific applications. Our experimental setup consists of a 32 node virtualized cluster with machines having CPU frequency between 2 GHz to 3 GHz. The framework was tested with a subset of NAS parallel benchmarks with the workload generated from Dror Feitelson’s workload archives. The prediction accuracy of our performance estimation model is over 80%. The framework implementation is lightweight, with an overhead of 3%. Our experiments show that we are able to improve the throughput of the compute farm by 25% and the time saved by the HC with our framework is over 30%. The framework can be readily extended to HCs supporting a cloud computing environment.

For several decades silica-based optical fibres have been used for telecommunication and sensor purposes. The single-mode fibre is frequently employed in long-distance networks, whereas the multi-mode fibre is the preferred means of signal transport in campus and in-building networks. Because of the huge bandwidth of optical fibres in comparison to its electrical wireless and copper-based counterparts, the demand for optical fibres keeps increasing. In a competitive market, fibre manufacturers aim to produce ever better fibres that are as cheap and easy to employ as possible. As fibre research, development and manufacturing is a mature discipline, improvements in fibre design can only be achieved through the construction of robust, accurate and efficient numerical fibre models for the computation of those quantities that determine the behaviour of the fibre. We have developed a modular software code, based on Maxwell’s equations, to compute these quantities in a vectorial full-wave way for both single-mode and multi-mode optical fibres. Key is the refractive-index profile, or, more specifically, the dopant profile, as it defines the propagation, splicing and bending-loss characteristics of the fibre. For the single-mode fibre, the fibre quantities that we have concentrated on are dispersion, dispersion slope, mode-field diameter, effective area, bending loss, effective and theoretical cut-off wavelength and MAC-value. We highlight one fibre quantity in particular, viz. the computation of the bending loss in a single-mode fibre. Many approximate modelling techniques have been developed to estimate this loss in a fast way. Our numerical scheme, however, is the first rigorous one, as we have performed a vectorial full-wave analysis of the bent optical fibre. In this context, triple integrals involving products of Bessel functions with large, complex order and argument appear. Due to cancellations in the pertaining computation, a high relative accuracy is needed for the computation of each product. As a result, it takes weeks on a contemporary computer to compute the bending loss as a function of the radius of curvature. We have used the vectorial full-wave bending-loss results to determine the most appropriate approximate method. Subsequently, we have extended that approximate method to compute the bending losses of higher-order modes, since the required effective cut-off wavelength depends on the bending loss of the first higher-order mode. The selected approximate method has been used in the ensuing bending-loss calculations. Since the fibre properties are often conflicting, it is a challenging task to adapt the radial dopant profile to meet a set of predefined design goals. A design goal is a combination of desired values for (some of) the aforementioned fibre quantities, and can mathematically be translated into a cost function. The minimisation of this cost function provides us with the optimal dopant profile for that specific set. For the single-mode fibre, we have performed this minimisation for piecewise-linear profiles, by employing various global and gradient-based local optimisation strategies to speed up the design step considerably. Frequently,these optimisation strategies lead to counter-intuitive dopant profile designs that could not have been contrived otherwise. We have selected a deliberate mix of several optimisation routines and have compared their performances. Perhaps the most important conclusion is that there still appears to be room for improvement in the design of the radial dopant profile of commercially available fibres. For the multi-mode fibre, vectorial full-wave optimisation is not feasible yet because of the long computation times for the large number of propagating modes. Still, our numerical scheme allows for a manual fine-tuning of the popular power-law profile to minimise differential mode delay. Further, we have included mode coupling and differential mode attenuation in our model to obtain intensity patterns that match closely with measurements. We have also analysed the influence of profile variations, e.g. on-axis dips and kinks, on the intensity pattern. A selective excitation of different mode groups in a multi-mode fibre, offers the possibility to create several independent transmission channels, and thus a higher information capacity. Recently, the feasibility of this so-called mode group diversity multiplexing technique has been demonstrated. Simulations provide us with a means to better understand its operation and possibly increase its efficiency. The channel separation may be enhanced by employing a lens between the fibre and the detector, which is called mode-selective spatial filtering. Our numerical simulations of a mode group diversity multiplexing link, with and without mode-selective spatial filtering, are in agreement with the measurements. The above discussion makes clear that the developed software code has a wide range of applicability. Moreover, it is built in a modular way and thus extensions, like the inclusion of more fibre quantities or different profile dopants, are straightforward.

Rich, semantically descriptive file attributes are valuable in many contexts, such as semantic namespaces and desktop search. Descriptive attributes help users to find files placed in seemingly-arbitrary locations by different applications. However, extracting semantic attributes from file contents is nontrivial. An alternative is to examine file provenance: how and when files are used, and the agents that use them.We study the extraction of semantic attributes from file provenance by applying data mining and machine learning techniques to file metadata. We show that provenance and other metadata predict semantic attributes such as file extensions. This complements previous work, which has shown that file extensions predict access patterns.

The application of Concurrency Theory to Systems Biology is in its earliest stage of progress. The metaphor of cells as computing systems by Regev and Shapiro opened the employment of concurrent languages for the modelling of biological systems. Their peculiar characteristics led to the design of many bio-inspired formalisms which achieve higher faithfulness and specificity. In this thesis we present pi@, an extremely simple and conservative extension of the pi-calculus representing a keystone in this respect, thanks to its expressiveness capabilities. The pi@ calculus is obtained by the addition of polyadic synchronisation and priority to the pi-calculus, in order to achieve compartment semantics and atomicity of complex operations respectively. In its direct application to biological modelling, the stochastic variant of the calculus, Spi@, is shown able to model consistently several phenomena such as formation of molecular complexes, hierarchical subdivision of the system into compartments, inter-compartment reactions, dynamic reorganisation of compartment structure consistent with volume variation. The pivotal role of pi@ is evidenced by its capability of encoding in a compositional way several bio-inspired formalisms, so that it represents the optimal core of a framework for the analysis and implementation of bio-inspired languages. In this respect, the encodings of BioAmbients, Brane Calculi and a variant of P Systems in pi@ are formalised. The conciseness of their translation in pi@ allows their indirect comparison by means of their encodings. Furthermore it provides a ready-to-run implementation of minimal effort whose correctness is granted by the correctness of the respective encoding functions. Further important results of general validity are stated on the expressive power of priority. Several impossibility results are described, which clearly state the superior expressiveness of prioritised languages and the problems arising in the attempt of providing their parallel implementation. To this aim, a new setting in distributed computing (the last man standing problem) is singled out and exploited to prove the impossibility of providing a purely parallel implementation of priority by means of point-to-point or broadcast communication.

The design of noise-free, low-pollutant combustion devices requires the understanding and the prediction of the combustion noise. The noise originates from the coupling between perturbations in the heat release rate with the oscillating gas (acoustic velocity). Prediction of combustion noise requires the transfer function (TF) that correlates the variation in the heat release rate of the ame with the perturbation (acoustic velocity). Computational costs prohibit an e??cient calculation of the TF by simulating all combustion phenomena associated with the ame dynamics. Simpli??ed theoretical models, such as the hydrodynamic models, allow a signi??cant reduction of the computation time and capture the main features of the ame front dynamics. The fundamental assumption of the hydrodynamic models is that the Bunsen ame, which is described as a thin layer ( ame front) separating the burnt from the unburnt gas, is attached at the burner rim. Within the thin layer approximation, the computation of the TF requires the ame area and, consequenctly, the time-dependent ame front position. By de??ning the ame front as the zero-level set of a distance function, the evolution of the ame front is described by a level set equation. The existent experiments and theoretic kinematic models based on the thin layer approximation (e.g., the G-equation model) provide contradictory information on the phase of the TF. Experiments suggest a low-pass ??lter behaviour of the gain of the TF and an increase of the TF's phase up to several ?? as the frequency increases. In contrast, most of the theoretical models indicate a saturation of the phase of the TF at the level of ??/2. Although the use of a convective wave model for the ow [80] leads to a better agreement between theory and experiments, the origin of the convective wave remains little understood. The discrepancies between theory and experiments most likely reside in the simpli??cations employed in the theoretical models. To understand the behaviour of the experimental TF, here we extend the theoretical models based on the G-equation approach. In the ??rst step, we extend the models by addressing ames that have an arbitrary cone angle and a burning velocity with variable direction. To carry out this ??rst extension we analyse the evolution of a Bunsen ame in a Poiseuille ow from an initially at pro??le to a stationary conical shape. The analysis leads to the correct derivation of the boundary conditions in the extended model employed for the ame evolution in a perturbed Poiseuille ow. We demonstrate that the new model proposed here improves the description of the front close to the boundary and, hence, the behaviour of the ame response to velocity perturbations. Because recent measurements [52] suggest that a better understanding of the TF's phase behaviour requires a hydrodynamic model that accounts for the moving edge of the ame, in the second step we extend the hydrodynamic model to account for non-attached ames. We model the ame front as an open curve by using two level set functions whose zero-level sets are locally normal at the edge point. The movement of the edge along the ame front is accounted for via a novel model for the edge speed. During computer simulations of the ame kinematics with the new extended model the local orthogonality of the level sets is preserved by employing a novel algorithm. The simulations demonstrate that our extended model qualitatively accounts for the ame stabilisation, the ame front and edge kinematics, and the stand-o?? distance of the ame above the burner rim.

Background and Purpose: Low back pain (LBP) is associated with paraspinal muscle dysfunctions. A method to study the deep lumbar paraspinal muscle activation is with intramuscular electromyography (EMG). However, it is currently unknown how paraspinal muscle performance is affected by the invasive intramuscular insertion and the presence of the fine-wire electrode in the muscle. The purpose of this study was to analyze how insertion of fine-wire EMG into lumbar paraspinal muscle affects the lumbar paraspinal muscle fatigue, endurance, activation, and peak extension torque during high exertion spinal extension exercises. Participants: 20 individuals between the ages of 18-40 participated. The participants were healthy with no history of LBP within the last 6 months that required activity modification or medical care. Methods: Data was obtained during 3 separate testing sessions, spaced 5 to 10 days apart. The first session obtained baseline outcome measures without intramuscular insertion (BL), with subsequent sessions utilizing a random order of insertion followed by leaving the intramuscular electrode fine-wire in (WI) or out (WO) of the muscle. Lumbar paraspinal peak extension torque was assessed with isokinetic dynamometry. Lumbar paraspinal endurance was evaluated using the Sorensen test. Paraspinal muscle fatigue was assessed using the rate of change (slope) of the median frequency during the endurance test. Percent of muscle activation was calculated by using the average muscle activation level during the endurance task. Pain and discomfort levels were recorded using the Visual Analog Scale (VAS) at specific times during the test sessions. All outcome measures were compared across the 3 conditions using one-way repeated measures ANOVAs and post-hoc analyses when indicated. Results: Our results showed no significant difference in peak torque (p = 0.196) between the BL, WI, and WO conditions. A significant difference in lumbar paraspinal endurance was found between the 3 conditions (p = 0.025). Post-hoc analysis showed that the muscle endurance in the WO condition was significantly longer than the BL condition (161.30 ± 58.267 sec vs. 142.05 ± 48.159 sec; p = 0.037). Percent of muscle activation during the endurance testing was not significantly different between the 3 conditions (p = 0.120). Pain scores reported during the 3 conditions were minimal (ranged 0-4/10). No pain was reported on the first day of testing (BL). No significant difference in pain scores was found between the WI and WO conditions: during each of the the three MVIC trials, after the MVIC trials, during the Sorensen test, or after the Sorensen test (p = 0.104, p = 0.186, p = 0.214, p = 0.330, p = 0.527, p = 0.481, respectively). Discussion: Our findings suggested that the insertion and presence of fine-wire EMG in the lumbar paraspinal muscles had no significant impact on lumbar paraspinal muscle peak extension torque, activation or fatigue and induced minimal pain. However, the results did suggest that the insertion and subsequent removal of the fine-wire did have an affect on lumbar paraspinal endurance. This study provides empirical evidence to validate the use of fine-wire EMG for studying lumbar paraspinal muscles during activities that require high muscular exertion.

Recently, the popular logical frameworks on strategy specification and verification in the multi-agent concurrent systems, such as alternating-time temporal logic and Strategy Logic (SL), mainly focus on the strategic abilities of one coalition. In them, the notion of strategy is just viewed as a pure syntax and/or semantics object, we cannot represent or reason about the internal structures of strategies, let alone strategic abilities under these ones. In this paper, based on linear dynamic logic, by extending SL, we propose a new strategic logic, named Dynamic Strategy Logic (DSL), which includes the existential/ universal quantification operators about regular expressions with test expressions. By introducing action atoms, we can specify both the evolution of time and structured strategies by means of regular expressions. Hence, in this logic, we can represent and reason about much more expressive strategic abilities under structured strategies of coalitions, and prove that DSL is more expressive than SL.