A Result on the Small Quasi-Kernel Conjecture

Any directed graph $D=(V(D),A(D))$ in this work is assumed to be finite and without self-loops. A source in a directed graph is a vertex having at least one ingoing arc. A quasi-kernel $Q\subseteq V(D)$ is an independent set in $D$ such that every vertex in $V(D)$ can be reached in at most two steps from a vertex in $Q$. It is an open problem whether every source-free directed graph has a quasi-kernel of size at most $|V(D)|/2$, a problem known as the small quasi-kernel conjecture (SQKC). The aim of this paper is to prove the SQKC under the assumption of a structural property of directed graphs. This relates the SQKC to the existence of a vertex $u\in V(D)$ and a bound on the number of new sources emerging when $u$ and its out-neighborhood are removed from $D$. The results in this work are of technical nature and therefore additionally verified by means of the Coq proof-assistant.Comment: 9 pages, a link to the Coq code is mentioned in the paper, submitted to Electronic Journal of Combinatoric

A Process Algebra for Supervisory Coordination

A supervisory controller controls and coordinates the behavior of different components of a complex machine by observing their discrete behaviour. Supervisory control theory studies automated synthesis of controller models, known as supervisors, based on formal models of the machine components and a formalization of the requirements. Subsequently, code generation can be used to implement this supervisor in software, on a PLC, or embedded microprocessor. In this article, we take a closer look at the control loop that couples the supervisory controller and the machine. We model both event-based and state-based observations using process algebra and bisimulation-based semantics. The main application area of supervisory control that we consider is coordination, referred to as supervisory coordination, and we give an academic and an industrial example, discussing the process-theoretic concepts employed.Comment: In Proceedings PACO 2011, arXiv:1108.145

Maximally permissive controlled system synthesis for non-determinism and modal logic

We propose a new technique for controlled system synthesis on non-deterministic automata for requirements in modal logic. Synthesis, as defined in this paper, restricts a behavioral specification of the uncontrolled system such that it satisfies a given logical expression, while adhering to the rules dictated by supervisory control such as maximal permissiveness and controllability. The applied requirement formalism extends Hennessy-Milner logic with the invariant and reachability modalities from Gödel-Löb logic, and is therefore able to express a broad range of control requirements, such as marker state reachability and deadlock-freeness. This paper contributes to the field of control synthesis by achieving maximal permissiveness in a non-deterministic context for control requirements in modal logic, and treatment of controllability via partial bisimulation. We present a well-defined and complete derivation of the synthesis result, which is supported further by computer-verified proofs created using the Coq proof assistant. The synthesis method is also presented in algorithmic form, including an analysis of its computational complexity. We show that the proposed synthesis theory allows full expressibility of Ramadge-Wonham supervisory control theory and we illustrate its applicability in two small industrial case studies, including an analysis with regard to scalability

On the Psychology of Perceived Procedural Justice : Experimental Evidence that Behavioral Inhibition Strengthens Reactions to Voice and No-Voice Procedures

This paper argues that when people try to sort out whether they are treated in just or unjust manners, they will tend to inhibit ongoing action to pause and check what is going on. In this way, behavioral inhibition can facilitate the procedural justice judgment process of interpreting whether you were treated in just or unjust ways. We further note that receiving opportunities to voice opinions is a key antecedent of perceived procedural justice. Following this line of reasoning, we argued that an experimental manipulation that strengthens behavioral inhibition should lead people to respond more strongly to receiving voice versus being withheld voice in decision-making procedures. In two studies, we found that reminding people of times they acted with public inhibitions (versus not reminding them) indeed led to more negative procedural judgments following no-voice procedures (Study 1) and to more positive procedural justice judgments following voice procedures (Study 2). These findings suggest that higher levels of behavioral inhibition may lead people to become more sensitive to what happens in their environments and, hence, affect the justice judgment process

On Why Procedural Justice Matters in Court Hearings: Experimental Evidence that Behavioral Disinhibition Weakens the Association between Procedural Justice and Evaluations of Judges

Using two randomized controlled courtroom experiments on actual litigants at court hearings, we examine a thus far unexplored reason why perceived procedural justice can be strongly associated with litigants' trust in judges and legitimate power assigned to judges. We argue that because litigants try to make sense of what is happening at their hearings, they will tend to inhibit ongoing action in order to pause and check what is going on in the courtroom. During this state of behavioral inhibition, experiences of how fairly judges are treating them will have a sturdy impact on litigants’ reactions. This explanation implies that an experimental manipulation known to weaken behavioral inhibition should attenuate the positive association between perceived procedural justice and trust and legitimacy ratings. The results of both experiments support this line of reasoning. We discuss the implications for the understanding of the psychology of procedural justice and the robustness of priming effects in experimental social psychology

On the Psychology of Perceived Procedural Justice : Experimental Evidence that Behavioral Inhibition Strengthens Reactions to Voice and No-Voice Procedures

This paper argues that when people try to sort out whether they are treated in just or unjust manners, they will tend to inhibit ongoing action to pause and check what is going on. In this way, behavioral inhibition can facilitate the procedural justice judgment process of interpreting whether you were treated in just or unjust ways. We further note that receiving opportunities to voice opinions is a key antecedent of perceived procedural justice. Following this line of reasoning, we argued that an experimental manipulation that strengthens behavioral inhibition should lead people to respond more strongly to receiving voice versus being withheld voice in decision-making procedures. In two studies, we found that reminding people of times they acted with public inhibitions (versus not reminding them) indeed led to more negative procedural judgments following no-voice procedures (Study 1) and to more positive procedural justice judgments following voice procedures (Study 2). These findings suggest that higher levels of behavioral inhibition may lead people to become more sensitive to what happens in their environments and, hence, affect the justice judgment process

On Why Procedural Justice Matters in Court Hearings: Experimental Evidence that Behavioral Disinhibition Weakens the Association between Procedural Justice and Evaluations of Judges

Using two randomized controlled courtroom experiments on actual litigants at court hearings, we examine a thus far unexplored reason why perceived procedural justice can be strongly associated with litigants' trust in judges and legitimate power assigned to judges. We argue that because litigants try to make sense of what is happening at their hearings, they will tend to inhibit ongoing action in order to pause and check what is going on in the courtroom. During this state of behavioral inhibition, experiences of how fairly judges are treating them will have a sturdy impact on litigants’ reactions. This explanation implies that an experimental manipulation known to weaken behavioral inhibition should attenuate the positive association between perceived procedural justice and trust and legitimacy ratings. The results of both experiments support this line of reasoning. We discuss the implications for the understanding of the psychology of procedural justice and the robustness of priming effects in experimental social psychology

Maximally permissive controlled system synthesis for modal logic

We propose a new method for controlled system synthesis on non-deterministic automata, which includes the synthesis for deadlock- freeness, as well as invariant and reachability expressions. Our technique restricts the behavior of a Kripke-structure with labeled transitions, representing the uncontrolled system, such that it adheres to a given requirement specification in an expressive modal logic, while all non-invalidating behavior is retained. This induces maximal permissiveness in the context of supervisory control. Research presented in this paper allows a system model to be constrained according to a broad set of liveness, safety and fairness specifications of desired behavior, and embraces most concepts from Ramadge-Wonham supervisory control, including controllability and marker-state reachability. The synthesis construction is formally verified using the Coq proof assistant