The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms

The literature specifies extensive-form games in many styles, and eventually I hope to formally translate games across those styles. Toward that end, this paper defines $\mathbf{NCF}$, the category of node-and-choice forms. The category's objects are extensive forms in essentially any style, and the category's isomorphisms are made to accord with the literature's small handful of ad hoc style equivalences. Further, this paper develops two full subcategories: $\mathbf{CsqF}$ for forms whose nodes are choice-sequences, and $\mathbf{CsetF}$ for forms whose nodes are choice-sets. I show that $\mathbf{NCF}$ is "isomorphically enclosed" in $\mathbf{CsqF}$ in the sense that each $\mathbf{NCF}$ form is isomorphic to a $\mathbf{CsqF}$ form. Similarly, I show that $\mathbf{CsqF_{\tilde a}}$ is isomorphically enclosed in $\mathbf{CsetF}$ in the sense that each $\mathbf{CsqF}$ form with no-absentmindedness is isomorphic to a $\mathbf{CsetF}$ form. The converses are found to be almost immediate, and the resulting equivalences unify and simplify two ad hoc style equivalences in Kline and Luckraz 2016 and Streufert 2019. Aside from the larger agenda, this paper already makes three practical contributions. Style equivalences are made easier to derive by [1] a natural concept of isomorphic invariance and [2] the composability of isomorphic enclosures. In addition, [3] some new consequences of equivalence are systematically deduced.Comment: 43 pages, 9 figure

The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms

The literature specifies extensive-form games in several styles, and eventually I hope to formally translate games across those styles. Toward that end, this paper defines NCF, the category of node-and-choice forms. The category's objects are game forms in any style, and the category's isomorphisms are made to accord with the literature's small handful of ad hoc style equivalences. More specifically, the paper develops two full subcategories: CsqF for forms whose nodes are choice-sequences, and CsetF for forms whose nodes are choice-sets. I show that NCF is ``isomorphically enclosed'' in CsqF in the sense that each NCF form is isomorphic to a CsqF form. Similarly, I show that CsqF_\tilde{a} is isomorphically enclosed in CsetF in the sense that each CsqF form with no-absentmindedness is isomorphic to a CsetF form. The converses are found to be almost immediate, and the resulting equivalences unify and simplify two ad hoc style equivalences in Kline and Luckraz (Economic Theory Bulletin, 2016) and Streufert (International Journal of Game Theory, forthcoming). Aside from the larger agenda, this paper makes three practical contributions. Style equivalences are made easier to derive by [1] a natural concept of isomorphic invariance and [2] the composability of isomorphic enclosures. In addition, [3] some new consequences of equivalence are systematically deduced

The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms

The literature specifies extensive-form games in several styles, and eventually I hope to formally translate games across those styles. Toward that end, this paper defines NCF, the category of node-and-choice forms. The category's objects are game forms in any style, and the category's isomorphisms are made to accord with the literature's small handful of ad hoc style equivalences. More specifically, the paper develops two full subcategories: CsqF for forms whose nodes are choice-sequences, and CsetF for forms whose nodes are choice-sets. I show that NCF is ``isomorphically enclosed'' in CsqF in the sense that each NCF form is isomorphic to a CsqF form. Similarly, I show that CsqF_\tilde{a} is isomorphically enclosed in CsetF in the sense that each CsqF form with no-absentmindedness is isomorphic to a CsetF form. The converses are found to be almost immediate, and the resulting equivalences unify and simplify two ad hoc style equivalences in Kline and Luckraz (Economic Theory Bulletin, 2016) and Streufert (International Journal of Game Theory, forthcoming). Aside from the larger agenda, this paper makes three practical contributions. Style equivalences are made easier to derive by [1] a natural concept of isomorphic invariance and [2] the composability of isomorphic enclosures. In addition, [3] some new consequences of equivalence are systematically deduced

Doctor of Philosophy

dissertationOver the last decade, cyber-physical systems (CPSs) have seen significant applications in many safety-critical areas, such as autonomous automotive systems, automatic pilot avionics, wireless sensor networks, etc. A Cps uses networked embedded computers to monitor and control physical processes. The motivating example for this dissertation is the use of fault- tolerant routing protocol for a Network-on-Chip (NoC) architecture that connects electronic control units (Ecus) to regulate sensors and actuators in a vehicle. With a network allowing Ecus to communicate with each other, it is possible for them to share processing power to improve performance. In addition, networked Ecus enable flexible mapping to physical processes (e.g., sensors, actuators), which increases resilience to Ecu failures by reassigning physical processes to spare Ecus. For the on-chip routing protocol, the ability to tolerate network faults is important for hardware reconfiguration to maintain the normal operation of a system. Adding a fault-tolerance feature in a routing protocol, however, increases its design complexity, making it prone to many functional problems. Formal verification techniques are therefore needed to verify its correctness. This dissertation proposes a link-fault-tolerant, multiflit wormhole routing algorithm, and its formal modeling and verification using two different methodologies. An improvement upon the previously published fault-tolerant routing algorithm, a link-fault routing algorithm is proposed to relax the unrealistic node-fault assumptions of these algorithms, while avoiding deadlock conservatively by appropriately dropping network packets. This routing algorithm, together with its routing architecture, is then modeled in a process-algebra language LNT, and compositional verification techniques are used to verify its key functional properties. As a comparison, it is modeled using channel-level VHDL which is compiled to labeled Petri-nets (LPNs). Algorithms for a partial order reduction method on LPNs are given. An optimal result is obtained from heuristics that trace back on LPNs to find causally related enabled predecessor transitions. Key observations are made from the comparison between these two verification methodologies

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems