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Algorithmic complexity is discussed as a computational counterpart to the second law of thermodynamics. It is shown that algorithmic complexity, which is a measure of randomness, sets limits on the thermodynamic cost of computations and casts a new light on the limitations of Maxwell's demon. Algorithmic complexity can also be used to define distance between binary strings.
The GRASP/Ada project (Graphical Representations of Algorithms, Structures, and Processes for Ada) has successfully created and prototyped an algorithmic level graphical representation for Ada software, the Control Structure Diagram (CSD), and a new visualization for a fine-grained complexity metric called the Complexity Profile Graph (CPG). By synchronizing the CSD and the CPG, the CSD view of control structure, nesting, and source code is directly linked to the corresponding visualization of statement level complexity in the CPG. GRASP has been integrated with GNAT, the GNU Ada 95 Translator to provide a comprehensive graphical user interface and development environment for Ada 95. The user may view, edit, print, and compile source code as a CSD with no discernible addition to storage or computational overhead. The primary impetus for creation of the CSD was to improve the comprehension efficiency of Ada software and, as a result, improve reliability and reduce costs. The emphasis has been on the automatic generation of the CSD from Ada 95 source code to support reverse engineering and maintenance. The CSD has the potential to replace traditional prettyprinted Ada source code. The current update has focused on the design and implementation of a new Motif compliant user interface, and a new CSD generator consisting of a tagger and renderer. The Complexity Profile Graph (CPG) is based on a set of functions that describes the context, content, and the scaling for complexity on a statement by statement basis. When combined graphicafly, the result is a composite profile of complexity for the program unit. Ongoing research includes the development and refinement of the associated functions, and the development of the CPG generator prototype. The current Version 5.0 prototype provides the capability for the user to generate CSDs and CPGs from Ada 95 source code in a reverse engineering as well as forward engineering mode with a level of flexibility suitable for practical application. This report provides an overview of the GRASP/Ada project with an emphasis on the current update.
Modern electronic imaging systems include optics, sensors, sampling, noise, processing, compression, transmission and display elements, and are viewed by the human eye. Many of these elements cannot be assessed by traditional imaging system metrics such as the MTF. More complex metrics such as NVTherm do address these elements, but do so largely through parametric adjustment of an MTF-like metric. The parameters are adjusted through subjective testing of human observers identifying specific targets in a set of standard images. We have designed a new metric that is based on a model of human visual pattern classification. In contrast to previous metrics, ours simulates the human observer identifying the standard targets. One application of this metric is to quantify performance of modern electronic periscope systems on submarines.
The national airspace has evolved over many years to accommodate increased traffic demand [1] while simultaneously maintaining one of the safest forms of transportation [2], [3]. One of the reasons for this success is the ability of the system and the operators to adapt and accommodate to situations that routinely disrupt optimal operations. These situations may include: adverse weather, delays, early arrivals, equipment outages, and other factors that are outside the operators ability to control. These factors can lead to states where automation is unable to properly handle these issues and therefore air traffic controllers and pilots have to intervene, ultimately increasing communication between operators resulting in higher workload. As controller workload increases to handle sub-optimal operating conditions this can be viewed as an increase in complexity. The reasoning for this is because humans are now required to make tactical decisions in response to external factors, resulting in a departure from the strategic plan where operations would be more efficiently managed. Human operators control airspace complexity under rigid regulations that are constantly changing. The airspace is divided into sectors and the number of aircraft assigned to each controller is limited for safe handling. There has been past work that devised airspace complexity metrics in commercial aviation and related these metrics to controller workload (e.g., [4],[5]). The upper bounds on the system load are pre-determined. Such bounds on complexity make for a safe system, but the system cannot scale and adapt to autonomous, dense, and heterogeneous traffic, including the many types of Unmanned Aerial Vehicles (UAVs) envisioned to be added to the operations. We hypothesize that, as traffic density and heterogeneity grow, and other key metrics change, there will be phase transitions at which the way traffic should be managed changes significantly [6]. We offer a method for in-time detection of contributing factors that lead to phase transitions, characterized by increased complexity. To the best of our knowledge, there is no tool similar to our proposed effort that identifies such contributing factors or precursor patterns. To define the scope we are proposing to measure complexity from the viewpoint of the Terminal Radar Approach Control Facilities (TRACON) controller’s perspective. In particular we are analyzing arrivals into KSFO. With safety as the top concern for airspace operators, it is important to recognize that as density and heterogeneity grow, the focus of the system will change. Times of the day when the airspace has low density and heterogeneity, the flights will follow more efficient paths where the aircraft move on established routes that are more or less directly to the destination. However, when density and heterogeneity increases, the system will begin changing focus to avoiding conflicts and collisions and route the flights in a more flexible way. Higher flexibility requires more communication and coordination between controllers and pilots which the current automation is unable to handle. This paper proposes a novel approach that monitors airspace complexity at multiple scales, uses a Machine Learning-based tool that predicts when operations will transition to a regime of greater complexity, and identifies actions that can reduce the complexity while still maintaining efficient and safe operations. We demonstrate our proposed approach using data from multiple complementary sources. This includes, but is not limited to: historical aircraft surveillance data from NASA’s Sherlock Data Warehouse [7], METAR weather data, and airport configuration data from Aviation System Performance Metrics (ASPM). The surveillance data flight paths are sampled at a variable sample rate — increasing as the aircraft approaches the airport. This is due to how Sherlock manages flight track stitching between different radar facilities which have different sampling rates. The weather and performance data are logged at defined intervals throughout the day at a courser refresh rate. In addition to the logged data and metrics, we leverage pre-defined Standard Terminal Arrival Routes (STARs) procedures to characterize the path of each flight. Each flight files for one of these routes in the flight plan well before entering the terminal airspace, and approximately follows the route until it leaves the STAR, typically on the final fix of a runway transition. However, most flights do not always fly the full STAR procedure to completion [8], but the majority do adhere to the fixes within the common route of the procedure. Our approach leverages fixes in the common route of each of the STARs to build a reference path to the airport. This allows us to characterize the flight paths in what we are defining as the “maneuvering area” (the airspace between the STAR and before the flight is lined up on the runway’s final approach) to determine how off nominal the flights are to calculate its complexity score. Determining airspace complexity is a concept that does not have a concrete answer. In designing this metric, we consider what increases the workload for the air traffic controllers. Consequently more specialized vectoring maneuvers results in higher workload. Accordingly, we start with a theory: each flight has a direct path it takes from the STAR’s common route to the final approach’s outer marker fix for the flight’s landing runway. It is important to note that the direct path is only used as a reference. If the majority of the flights have a large consistent offset as compared to other routes it does not necessarily mean that those flights have higher complexity. We are merely building a distribution based on this direct path for that particular STAR and runway pair to determine the normal mode of operations for that route. Flights that are in the upper tail of these distributions will result in higher complexity scores and flights that fly in the median will represent the normal mode of operations and therefore will have lower complexity scores. Since flights following each STAR route take different paths to the airport, we have a different distribution for each STAR route and therefore can model these distributions to compute a complexity score from their respective normalized distributions. To evaluate the effectiveness of our proposed airspace complexity metric we will compare against an established approach based on trajectory clustering [9]. This unsupervised learning technique consists of the following steps: (1) identify the general maneuvering areas (waypoints) by performing $\kappa$-means or DBSCAN clustering on locations where aircraft frequently turn based on the surveillance radar track data, (2) map flight trajectories onto sequences of waypoints, and (3) cluster the sequences based on their common subsequences. From a high-level perspective, this baseline model learns nominal operations in the airspace through the sequence of waypoints that are representative of where aircraft change direction and defines deviations from the nominal operations as “complex.” Therefore, more deviations from the nominal operations correspond to higher complexity values. For our validation, we re-implemented this technique and tune model hyper-parameters to correctly detect waypoints for the arrival traffic into the San Francisco bay area. We will compute the complexity measure over a one-year period using our proposed technique as well as the baseline. Our validation will be based on each technique’s ability to detect a set of undesirable outcomes (e.g., go-arounds, holding patterns, average time in the airspace, etc.). Since our current complexity metric is derived from the offset from the direct reference path, it’s important to understand what causes these offsets. In many of the flights with high offset distance, flights performing holding patterns and S turns can be observed. These maneuvering tactics are utilized to add distance between the aircraft and the destination runway to prevent multiple flights from having conflicting arrival times. In order to predict a rise in complexity (or the precursor to complexity), it’s necessary to be able to identify these potential conflicts (which in turn, result in higher offsets). To do this, we define a “representative flight” for each STAR route and runway pair. This flight is approximately the path the flight would take if there was a clear path with no other flights in the airspace — including the time remaining to the airport. We first identify the flights for a given STAR runway pair using the offset to the reference path distributions that fall between the 44-55 percentiles. This yields the flights that conform to the most normal mode of operation. Each of these flights is partitioned based on the percent complete from the entry point into the maneuvering areas from 0\% – 100\% complete. Then for each percent “bin”, we take the median value of the flight’s latitude/longitude coordinates, airspeed, and (non causal) time remaining to the airport to construct a lookup table for each percent complete bin on a given route. As a flight enters the maneuvering area, we can find the estimated arrival time of a flight to the airport by finding the closest point to the representative path’s percent complete bin (relative to the flight’s current position at any snapshot in the airspace) and therefore retrieve the corresponding remaining time left on the “representative path”. We assume that the flight will follow the representative path to completion when deriving these estimates. We can then compare these estimated arrival times against other flights for the same snapshot in time to identify potential conflicts. If more flights are estimated to arrive within a tolerance window than there are runways available, then we have a potential conflict. We can use this derived measure along with other factors expected to add disruption to the operation such as weather and runway configuration changes as an input to machine learning tools to detect precursors that increases in our complexity measure. This novel method will assist in uncovering insights into the contributing factors that lead to increased complexity that may allow for in-time responses to avoid reaching a high complexity state in the airspace.
In this paper we introduce a new complexity metric to predict -in real-time- sector complexity for trajectory-based operations (TBO). TBO will be implemented in the Next Generation Air Transportation System (NextGen). Trajectory-Based Complexity (TBX) is a modified aircraft count that can easily be computed and communicated in a TBO environment based upon predictions of aircraft and weather trajectories. TBX is scaled to aircraft count and represents an alternate and additional means to manage air traffic demand and capacity with more consideration of dynamic factors such as weather, aircraft equipage or predicted separation violations, as well as static factors such as sector size. We have developed and evaluated TBX in the Airspace Operations Laboratory (AOL) at the NASA Ames Research Center during human-in-the-loop studies of trajectory-based concepts since 2009. In this paper we will describe the TBX computation in detail and present the underlying algorithm. Next, we will describe the specific TBX used in an experiment at NASA's AOL. We will evaluate the performance of this metric using data collected during a controller-inthe- loop study on trajectory-based operations at different equipage levels. In this study controllers were prompted at regular intervals to rate their current workload on a numeric scale. When comparing this real-time workload rating to the TBX values predicted for these time periods we demonstrate that TBX is a better predictor of workload than aircraft count. Furthermore we demonstrate that TBX is well suited to be used for complexity management in TBO and can easily be adjusted to future operational concepts.
Thirty audiometrically screened test participants judged the relative annoyance of two comparison (variable level) and thirty-four standard (fixed level) signals in an adaptive paired comparison psychoacoustic study. The signal ensemble included both FAR Part 36 Stage 2 and 3 aircraft overflights, as well as synthesized aircraft noise signatures and other non-aircraft signals. All test signals were presented for judgment as heard indoors, in the presence of continuous background noise, under free-field listening conditions in an anechoic chamber. Analyses of the performance of 30 noise metrics as predictors of these annoyance judgments confirmed that the more complex metrics were generally more accurate and precise predictors than the simpler methods. EPNL was somewhat less accurate and precise as a predictor of the annoyance judgments than a duration-adjusted variant of Zwicker's Loudness Level.
The national airspace has evolved over many years to accommodate increased traffic demand while simultaneously maintaining air travel as one of the safest forms of transportation. One of the reasons for this success is the ability of the air traffic control system and the operators to adapt and accommodate to situations that routinely disrupt normal operations. These situations may include: adverse weather, delays, early arrivals, equipment outages, and other factors that are outside the operators’ ability to control. These factors can lead to states where automation is unable to properly handle these issues, and therefore air traffic controllers and pilots have to intervene — ultimately increasing communication between operators resulting in higher workload. As controller workload increases to handle sub-optimal operating conditions, complexity increases. This is because, under these conditions humans are required to make tactical decisions in response to external factors. This results in a departure from the original strategic plan where operations would be more efficiently managed. Human operators manage airspace complexity under rigid regulations but in a constantly changing environment. The airspace is divided into sectors and the number of aircraft assigned to each controller is limited for safe handling. Some prior studies devised airspace complexity metrics in commercial aviation and related these metrics to controller workload. The upper bounds on the system load are pre-determined. Such bounds on complexity make for a safe system, but the system cannot scale and adapt to autonomous, dense, and heterogeneous traffic — including the many types of Unmanned Aerial Vehicles (UAVs) envisioned to be added to the operations. We hypothesize that, as traffic density and heterogeneity grow, and other key metrics change, there will be phase transitions at which the way traffic should be managed changes significantly. We offer a method for in-time detection of contributing factors that lead to phase transitions, characterized by increased complexity. To the best of our knowledge, there is no tool similar to ours that identifies such contributing factors or precursor patterns.
This paper investigates the oversimplification of the inherently complex systems engineering process in space life support. The standard systems engineering process steps are described. The International Space Station (ISS) life support system is explained with its goals and performance criteria. Although it is not usually emphasized, the essential function of developing a hierarchy of systems and subsystems is to simplify the design process. The System Complexity Metric (SCM) shows how this di-vide-and-conquer approach also reduces the system complexity. The complete systems engineering process has many detailed steps. It is often simplified because of the effort required and the human limitations on working memory and decision span. Systems analysis demands slow, logical, and fo-cused thinking but is often bypassed in favor of quick, intuitive, subconscious “gut feel.” A study of 100 system designs found examples of 12 specific mental mistakes, such as ignoring stakeholder needs, and these mistakes are essentially oversimplifications of the systems engineering process. An analysis of space life support goals, options, criteria, and processes found 11 examples of oversimplifications in systems engineering, such as neglecting safety and cost. All these 11 oversimplifications could be traced to one or more of the 12 previously identified mental mistakes or other well-known ones, such as ig-noring sunk costs. Oversimplification of the systems engineering process is rarely noticed but is a common and harmful problem. A study of failures in 50 different space systems found that problems in systems engineering caused failures and often led to errors in design, development, and test that further contributed to failure. It seems that more diligent systems engineering could prevent many project problems and failures, but projects seem to be more guided by “gut feel” based on tradition, authority, and consensus than on the logical, rational systems engineering approach.
The distributions and relationships derived from the change data collected during the development of a medium scale satellite software project show that meaningful results can be obtained which allow an insight into software traits and the environment in which it is developed. Modified and new modules were shown to behave similarly. An abstract classification scheme for errors which allows a better understanding of the overall traits of a software project is also shown. Finally, various size and complexity metrics are examined with respect to errors detected within the software yielding some interesting results.
The distributions and relationships derived from the change data collected during the development of a medium scale satellite software project show that meaningful results can be obtained which allow an insight into software traits and the environment in which it is developed. Modified and new modules were shown to behave similarly. An abstract classification scheme for errors which allows a better understanding of the overall traits of a software project is also shown. Finally, various size and complexity metrics are examined with respect to errors detected within the software yielding some interesting results.
The impact of software structure on maintainability aspects including comprehensibility, locality, modifiability, and reusability in a distributed system environment is studied in a controlled maintenance experiment involving six medium-size distributed software systems implemented in LADY (language for distributed systems) and six in an extended version of sequential PASCAL. For all maintenance aspects except reusability, the results were quantitatively given in terms of complexity metrics which could be automated. The results showed LADY to be better suited to the development of maintainable software than the extension of sequential PASCAL. The strong typing combined with high parametrization of units is suggested to improve the reusability of units in LADY.
This paper introduces a ground delay based traffic management approach to reduce the impedance based airspace complexity for a given scenario. The preliminary work presented here extends our prior research on developing an impedance based complexity metric for unmanned aircraft system traffic scenario classification. Impedance based metric was evaluated for 1045 randomly-generated scenarios. Scenarios with overall impedance above a certain threshold were declared as no-go. A ground delay approach was developed to be applied to the rest of the scenarios so as to remediate any scenarios with small areas of high impedance on their impedance maps. A sample application is shown for a scenario with sixty flights. The final paper will include detailed trade-offs between overall accrued system delay and the delay tolerance for each aircraft. A sample application to a potential Urban Air Mobility traffic scenario will also be included in the final paper.
This paper introduces a ground-delay-based traffic management approach to reduce the impedance-based airspace complexity for a given scenario. This work extends our prior research on developing an impedance-based complexity metric for unmanned aircraft system traffic scenario classification. Impedance-based metric was evaluated for 1045 randomly generated scenarios. Scenarios with overall impedance above a certain threshold were declared as not feasible. A ground-delay-based approach was developed to be applied to the rest of the scenarios so as to remediate any scenarios with small areas of high impedance on their impedance maps. A sample application is shown for a scenario with sixty flights. The detailed trade-offs between overall accrued system delay, the number of delayed flights, the total number of conflicts and the highest impedance observed as a function of the delay tolerance for each aircraft are provided. Potential applications to Urban Air Mobility traffic scenarios are also discussed.
Flight research has shown the effectiveness of adaptive flight controls for improving aircraft safety and performance in the presence of uncertainties. The National Aeronautics and Space Administration's (NASA)'s Integrated Resilient Aircraft Control (IRAC) project designed and conducted a series of flight experiments to study the impact of variations in adaptive controller design complexity on performance and handling qualities. A novel complexity metric was devised to compare the degrees of simplicity achieved in three variations of a model reference adaptive controller (MRAC) for NASA's F-18 (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) Full-Scale Advanced Systems Testbed (Gen-2A) aircraft. The complexity measures of these controllers are also compared to that of an earlier MRAC design for NASA's Intelligent Flight Control System (IFCS) project and flown on a highly modified F-15 aircraft (McDonnell Douglas, now The Boeing Company, Chicago, Illinois). Pilot comments during the IRAC research flights pointed to the importance of workload on handling qualities ratings for failure and damage scenarios. Modifications to existing pilot aggressiveness and duty cycle metrics are presented and applied to the IRAC controllers. Finally, while adaptive controllers may alleviate the effects of failures or damage on an aircraft's handling qualities, they also have the potential to introduce annoying changes to the flight dynamics or to the operation of aircraft systems. A nuisance rating scale is presented for the categorization of nuisance side-effects of adaptive controllers.
The growing demand for air travel is increasing the need for mitigating air traffic congestion and complexity problems, which are already at high levels. At the same time new surveillance, navigation, and communication technologies are enabling major transformations in the air traffic management system, including net-based information sharing and collaboration, performance-based access to airspace resources, and trajectory-based rather than clearance-based operations. The new system will feature different schemes for allocating tasks and responsibilities between the ground and airborne agents and between the human and automation, with potential capacity and cost benefits. Therefore, complexity management requires new metrics and methods that can support these new schemes. This paper presents metrics and methods for preserving trajectory flexibility that have been proposed to support a trajectory-based approach for complexity management by airborne or ground-based systems. It presents extensions to these metrics as well as to the initial research conducted to investigate the hypothesis that using these metrics to guide user and service provider actions will naturally mitigate traffic complexity. The analysis showed promising results in that: (1) Trajectory flexibility preservation mitigated traffic complexity as indicated by inducing self-organization in the traffic patterns and lowering traffic complexity indicators such as dynamic density and traffic entropy. (2)Trajectory flexibility preservation reduced the potential for secondary conflicts in separation assurance. (3) Trajectory flexibility metrics showed potential application to support user and service provider negotiations for minimizing the constraints imposed on trajectories without jeopardizing their objectives.
Software analysis tools and techniques often leverage structural code coverage information to reason about the dynamic behavior of software. Existing techniques instrument the code with the required structural obligations and then monitor the execution of the compiled code to report coverage. Instrumentation based approaches often incur considerable runtime overhead for complex structural coverage metrics such as Modified Condition/Decision (MC/DC). Code instrumentation, in general, has to be approached with great care to ensure it does not modify the behavior of the original code. Furthermore, instrumented code cannot be used in conjunction with other analyses that reason about the structure and semantics of the code under test. In this work, we introduce a non-intrusive preprocessing approach for computing structural coverage information. It uses a static partial evaluation of the decisions in the source code and a source-to-bytecode mapping to generate the information necessary to efficiently track structural coverage metrics during execution. Our technique is flexible; the results of the preprocessing can be used by a variety of coverage-driven software analysis tasks, including automated analyses that are not possible for instrumented code. Experimental results in the context of symbolic execution show the efficiency and flexibility of our nonintrusive approach for computing code coverage information
All complex development projects experience delays and corresponding backlogs of their project control milestones during their acquisition lifecycles. NASA Goddard Space Flight Center (GSFC) Flight Projects Directorate (FPD) teamed with The Aerospace Corporation (Aerospace) to develop a collection of Early Warning Look Ahead metrics that would provide GSFC leadership with some independent indication of the programmatic health of GSFC flight projects. As part of the collection of Early Warning Look Ahead metrics, the Percent Milestone Backlog metric is particularly revealing, and has utility as a stand-alone execution performance monitoring tool. This paper describes the purpose, development methodology, and utility of the Percent Milestone Backlog metric. The other four Early Warning Look Ahead metrics are also briefly discussed. Finally, an example of the use of the Percent Milestone Backlog metric in providing actionable insight is described, along with examples of its potential use in other commodities.
Upper Class E Traffic Management (ETM) is envisioned to cooperatively facilitate operations of a diverse set of aerial vehicles, such as high-altitude long-endurance fixed-wing unmanned aircraft (low-speed and high-speed), high-altitude platforms, airships, stratospheric balloons, supersonic unmanned and commercial aircraft, etc., with a wide variety of mission types, performance characteristics, communication, navigation and surveillance capabilities, maneuverability, and on-board avionics in the National Airspace System (NAS) ’above’ 60,000 feet above mean sea level, without an active and direct control from human air traffic controllers. A diverse mixture of aerial vehicle types creates significant challenges in understanding air traffic complexity, which may not correlate strongly with air traffic density. One key step for determining air traffic complexity in upper class E airspace is to first understand pairwise deconfliction metrics such as reachability, reserve area, and reserve flight time for each pair of unique aerial vehicle types under potential conflict. Therefore, pairwise deconfliction metrics are first defined, and analytical equations are derived for conflict resolution using the heading change maneuver. Next, case studies are performed to analyze deconfliction metrics to avoid secondary conflicts in upper class E airspace. The study shows that pairwise deconfliction metrics are functions of maneuverability, performance characteristics, uncertainty in position and velocity, heading angle change, and conflict angle of aerial vehicles. The next step for this research is to build a mathematical model for air traffic complexity using pairwise deconfliction metrics and validate it in an upper Class E simulation environment.