# TAIS

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Theoretical Analysis of Information Systems¹ is a published approach to mathematical modeling of a general enterprise information system based on systems theory and algebra. Its results are basic and startling only to the degree in which something like what the book does has not become an element of common IS practice.

## Studentenliiteratur

The TOC as reproduced below does not capture the incidence string style of the Auerbach original text, for example "Boundary Operator for Generalized Systems" in the original is marked § "12.31".

1. Systems Theory
1. Basic Problems of Systems Theory
1. Needs for a Formal Systems Theory
2. Common Faults in Systems Design Analysis
3. Different Kinds of Systems Study
4. Systems Engineering
5. Structural Systems Theory, Electric Networks and Elastic Systems
6. Mathematical Systems Theory as a System
7. Other Kinds of System Study
8. Elements of a Systems Theory
9. Usefulness of our Concise Definition of Systems
10. The Systems Analysis Approach
11. The Fundamental Principle of Systems Work
12. General and Special Properties of System Problems
13. Systems, Subsystems, Parts, and Boundaries
14. Structure Types of a System
15. System Partitioning
16. Systems Partitioning of Outer Boundary
17. A Sketch of a Basic Theory of Systems Analysis
18. The Suitable Number of Subsystems in a System
2. Systems Algebra
1. Algebraic Tools for Describing Systems
2. Precedemce Operator of a System (or Graph)
3. The Precdence Matrix of a System
4. The Precendents of s set of Parts
5. Use of the Precedence Matrix P to Determine the Precedents of a Set of parts
6. Connections with a Linked Data Structure
7. Matrix by Matrix Composition pn, n-th Precedents and Paths
8. Succedence Matrix PT
9. Generalization of the Precendence Concept
10. A generalized Matrix by Vector Operation
11. Generalized Matrices
12. Matrix Operations as Processing of Data Structures
13. Other Kinds of Algorithms for Processing Data Structures
14. P11, the 1-dimensional Precendence Matrix
15. P01 and P10, Precendence Matrices for Mixed 0-1 and 1-0 Dimension Respectively
16. Relations between P01, P10, P11, and P00 Respectively
17. Definition of E10, the Incidence Matrix
18. Boundary Operations on a System and the Incidence Matrix
19. Co-boundary Operation and Incidence Matrix
20. The Coincidence Matrix M10
21. Data Structure Representations of Incidence and Coincidence Matrices
22. Illustrations of Boundary Operations in Accounting
23. Built-up Systems and Gross Systems
24. System Connections, Boundary Operation and Cycles
25. Positional Operator for the System Graph
26. Simple Paths and Closed Paths in a System Graph
27. Transposed Positional Operator, Forward Positioning
28. General Positioning
29. Requirements Computation and Scheduling
30. Determining the Boundary Operator from M10 and the Part Boundary Operator RT
31. Boundary Operator for Generalized Systems
2. Information Systems Theory
1. Information Systems
1. Information Systems Design
2. Formalization of Information Systems Design
3. Component Problems of Information Systems
2. The Function of an Information System
1. The Function of an Information System
2. Two Tasks of an Information System
3. Operative Information Requirments. An Example.
4. The value of Directive Information
5. Effect of time for Decomposing. Executive Decisions.
6. Transient Decision Situation. Satisficing.
7. Information Needed in a Simplified Model of a Manufacturing Shop
3. The Economic Quantity of Information and Processing
1. The Economic Quantity of Information and Processing
2. Information Value as an Information Systems Design Parameter
3. Information and System Control
4. The Meaning of Information within a System
5. The Value of Information in a System
6. Data Representation aof Information in a System. Volume of Data
7. The Information System for a Simple Inventory
8. Operative vs. Directive Information
9. An Example of Optimum Reduction. Information Processing for a Simple Inventory
10. Information System for a Simple Work Station
4. Some Problems of Information Systems Design
1. Complexity of an Information System
5. Precedence Relations between Information Sets in and Information System
1. Data Structure of an Information System
2. On the Definition of Elementary Files (e-files)
3. Inference Problem in Information Systems Design
4. A Further Illustration [of] Information Precedence and Elementary File Definition; Computation of Weekly Wage
5. Cost Distribution of Job Costs as Another Illustration of Discussing Elementary Files
6. Identification of Precedence Information
7. Use of the Information Precedence Matrix P00 for Compatibility Checking
8. Some Other Uses of the Precedence Matrix P
9. The Precedence Structure and the Dynamic Flow of Processing
10. Completeness Theorem of Information Precedence
11. Systematic Design of a Directive Information System
6. Data and Information Files
1. Data and Information Files
2. Size of Data Terms and Precision Required
7. Files, Computations, and Processes
1. Files and Processes
2. The Size of a File
3. File Volume and Transport Volume, Processing Period
4. Transport Factor
5. Topological Transport Factor
6. Grouping of Computations into [O]ne Process
7. Incidence Matrix of Processes and Files
8. Effect of a Process Grouping
1. Effect of Process Grouping on the Transport Factor
2. Memory Requirement Associated with Process Grouping
3. Computer Programs and Memory Space for a Process
4. Example of a Process Grouping with Memory Limitation
9. File Consolidation
1. Reducing the Number of Transport Equipment Units
2. The Effect of File Consolidation in Direct-Access Stores
3. Effects of the Size of File Blocks (Physical Records)
4. The Effect upon CPU-time
5. Conclusion about File Consolidation and Choice of Block Sizes
6. Adaptation to Hardware Systems
10. System Design Computation Using Matrix Algebra
1. Information Systems Design Computations
2. Joining Rows in E10 to Represent Grouping of Process
3. Representing Process Grouping by a Generalized Matrix Operation
4. Matrix Operation to Compute File Transport
5. Calculations for Minimum File Transport Design
6. Procedures for Aiding the Intuitive System Design Phases
7. Defining File Consolidation by Matrix Operation on E10
8. Influences on Programming Language Development
11. File Storage Considerations
1. Files in Systems Using Mass Memories of Psuedo Random Access
2. Direct Processing versus Batched Processing
12. File Organizations
1. Record Layouts
2. Record Organization
13. System Reliability
1. Reliability of an Information System
2. Means for Checking Input Data
14. The Problem of Optimum Grouping of Information Process
3. Some Data Processing Problems
1. Relation between a Process and its Files
1. Relation between a Process and its Files
2. Some basic problems of File Processing
3. K-Progressive Process
4. Rectangular File Processing and Group Access
5. Retrieval of File Records for a Process
2. Influence of Word Structure
1. Influence of Word Length on Tape Recording Speed

This TOC, as reproduced here, is the normative designation by which I reference the text of the original document, not the original section numbering. A small number of copies of the work appear to be available online. The reader may safely take this TOC as a surrogate for the work under the presumption that its use as noted below will make its content clear and I have provided synoptic pages here for the critical sections.

## Import

TAIS is significant for several obvious reasons. One is historical. The work was published shortly after the introduction of the concept of Software Engineering and before the emergence of OOP, Design Patterns, and other currents which came to represent the mainstream of of systems analysis and design practice. Since Langefors actually developed his system during the even earlier period and thus to some extent its time and space complexity concerns seem archaic. The approach was developed over some time before the mid-1970s and so reflects a relatively low-level focus that seems quaint in a modern context. However the material culminating in the chapter on System Design Computation is of enduring value. I believe Langefors died a few years before the turn of the century and there was both a final work by him, related work by colleagues in Regnecentralen and other organizations, and related work from unrelated sources.

The work would probably not be acceptable in the computer science community of today as it exposits a mathematical treatment of systems analysis without actually providing details of that math. This doesn't detract from its intrinsic value and is even an advantage as it doesn't offer anything to undo in basing on operational elements now existing which can provide same.

## Role in ai-integration.biz

TAIS is a theoretical antecedent of the general approach to information systems development in ai-integration.biz.

## Further Reading

¹ Lagefors, B. Fourth Edition, AUERBACH. 1973 ISBN 0-87769-151-7