9,634 research outputs found
A Unifying Theory for Graph Transformation
The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO
Cyclic proof systems for modal fixpoint logics
This thesis is about cyclic and ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.Cyclic and ill-founded proof-theory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of cyclic companionship; and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one
UMSL Bulletin 2023-2024
The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp
Wind Riders of the Lost River Range: A Modular Project-Based Case for Software Development
The Wind Riders of the Lost River Range (WRLRR) is a modular project-based simulated case study. This case study is designed to accompany a hands-on collaborative semester project for a variety of software development courses. The case can be used in courses like Systems Analysis and Design, Database Design, Software Engineering, and Software Development. The case provides a detailed account of a situation that closely simulates a real-world problem. This challenging experiential learning opportunity reinforces course concepts through their application in a realistic scenario. WRLRR has been developed using the modular design of teaching case studies approach. This approach makes it possible to swap modules in and out of the case. This reduces instructor workload by making it unnecessary to develop a new case from scratch for each course iteration. It also discourages students from recycling solutions from previous courses because the case scenario has been altered. Adding or removing modules makes it possible to sufficiently vary the case study to refine the problem being addressed. Macros are provided to automate, and thereby facilitate, the insertion of modules
Language integrated relational lenses
Relational databases are ubiquitous. Such monolithic databases accumulate large
amounts of data, yet applications typically only work on small portions of the data
at a time. A subset of the database defined as a computation on the underlying
tables is called a view. Querying views is helpful, but it is also desirable to update
them and have these changes be applied to the underlying database. This view
update problem has been the subject of much previous work before, but support
by database servers is limited and only rarely available.
Lenses are a popular approach to bidirectional transformations, a generalization
of the view update problem in databases to arbitrary data. However, perhaps surprisingly, lenses have seldom actually been used to implement updatable views in
databases. Bohannon, Pierce and Vaughan propose an approach to updatable views called relational lenses. However, to the best of our knowledge this
proposal has not been implemented or evaluated prior to the work reported in
this thesis.
This thesis proposes programming language support for relational lenses. Language integrated relational lenses support expressive and efficient view updates,
without relying on updatable view support from the database server. By integrating relational lenses into the programming language, application development
becomes easier and less error-prone, avoiding the impedance mismatch of having
two programming languages. Integrating relational lenses into the language poses
additional challenges. As defined by Bohannon et al. relational lenses completely
recompute the database, making them inefficient as the database scales. The
other challenge is that some parts of the well-formedness conditions are too general for implementation. Bohannon et al. specify predicates using possibly infinite
abstract sets and define the type checking rules using relational algebra.
Incremental relational lenses equip relational lenses with change-propagating semantics that map small changes to the view into (potentially) small changes
to the source tables. We prove that our incremental semantics are functionally
equivalent to the non-incremental semantics, and our experimental results show
orders of magnitude improvement over the non-incremental approach. This thesis introduces a concrete predicate syntax and shows how the required checks
are performed on these predicates and show that they satisfy the abstract predicate specifications. We discuss trade-offs between static predicates that are fully
known at compile time vs dynamic predicates that are only known during execution and introduce hybrid predicates taking inspiration from both approaches.
This thesis adapts the typing rules for relational lenses from sequential composition to a functional style of sub-expressions. We prove that any well-typed
functional relational lens expression can derive a well-typed sequential lens.
We use these additions to relational lenses as the foundation for two practical implementations: an extension of the Links functional language and a library written
in Haskell. The second implementation demonstrates how type-level computation can be used to implement relational lenses without changes to the compiler.
These two implementations attest to the possibility of turning relational lenses
into a practical language feature
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
UMSL Bulletin 2022-2023
The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp
Barrier-Based Test Synthesis for Safety-Critical Systems Subject to Timed Reach-Avoid Specifications
We propose an adversarial, time-varying test-synthesis procedure for
safety-critical systems without requiring specific knowledge of the underlying
controller steering the system. From a broader test and evaluation context,
determination of difficult tests of system behavior is important as these tests
would elucidate problematic system phenomena before these mistakes can engender
problematic outcomes, e.g. loss of human life in autonomous cars, costly
failures for airplane systems, etc. Our approach builds on existing,
simulation-based work in the test and evaluation literature by offering a
controller-agnostic test-synthesis procedure that provides a series of
benchmark tests with which to determine controller reliability. To achieve
this, our approach codifies the system objective as a timed reach-avoid
specification. Then, by coupling control barrier functions with this class of
specifications, we construct an instantaneous difficulty metric whose minimizer
corresponds to the most difficult test at that system state. We use this
instantaneous difficulty metric in a game-theoretic fashion, to produce an
adversarial, time-varying test-synthesis procedure that does not require
specific knowledge of the system's controller, but can still provably identify
realizable and maximally difficult tests of system behavior. Finally, we
develop this test-synthesis procedure for both continuous and discrete-time
systems and showcase our test-synthesis procedure on simulated and hardware
examples
Investigations into Proof Structures
We introduce and elaborate a novel formalism for the manipulation and
analysis of proofs as objects in a global manner. In this first approach the
formalism is restricted to first-order problems characterized by condensed
detachment. It is applied in an exemplary manner to a coherent and
comprehensive formal reconstruction and analysis of historical proofs of a
widely-studied problem due to {\L}ukasiewicz. The underlying approach opens the
door towards new systematic ways of generating lemmas in the course of proof
search to the effects of reducing the search effort and finding shorter proofs.
Among the numerous reported experiments along this line, a proof of
{\L}ukasiewicz's problem was automatically discovered that is much shorter than
any proof found before by man or machine.Comment: This article is a continuation of arXiv:2104.1364
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