Strategic (Timed) Computation Tree Logic

We define extensions of CTL and TCTL with strategic operators, called Strategic CTL (SCTL) and Strategic TCTL (STCTL), respectively. For each of the above logics we give a synchronous and asynchronous semantics, i.e., STCTL is interpreted over networks of extended Timed Automata (TA) that either make synchronous moves or synchronise via joint actions. We consider several semantics regarding information: imperfect (i) and perfect (I), and recall: imperfect (r) and perfect (R). We prove that SCTL is more expressive than ATL for all semantics, and this holds for the timed versions as well. Moreover, the model checking problem for SCTL[ir] is of the same complexity as for ATL[ir], the model checking problem for STCTL[ir] is of the same complexity as for TCTL, while for STCTL[iR] it is undecidable as for ATL[iR]. The above results suggest to use SCTL[ir] and STCTL[ir] in practical applications. Therefore, we use the tool IMITATOR to support model checking of STCTL[ir]

Timed Parity Games: Complexity and Robustness

We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose a time delay and an action, and the action with the shorter delay is chosen. To prevent a player from winning by blocking time, we restrict each player to play strategies that ensure that the player cannot be responsible for causing a zeno run. First, we present an efficient reduction of these games to \emph{turn-based} (i.e., not concurrent) \emph{finite-state} (i.e., untimed) parity games. Our reduction improves the best known complexity for solving timed parity games. Moreover, the rich class of algorithms for classical parity games can now be applied to timed parity games. The states of the resulting game are based on clock regions of the original game, and the state space of the finite game is linear in the size of the region graph. Second, we consider two restricted classes of strategies for the player that represents the controller in a real-time synthesis problem, namely, \emph{limit-robust} and \emph{bounded-robust} winning strategies. Using a limit-robust winning strategy, the controller cannot choose an exact real-valued time delay but must allow for some nonzero jitter in each of its actions. If there is a given lower bound on the jitter, then the strategy is bounded-robust winning. We show that exact strategies are more powerful than limit-robust strategies, which are more powerful than bounded-robust winning strategies for any bound. For both kinds of robust strategies, we present efficient reductions to standard timed automaton games. These reductions provide algorithms for the synthesis of robust real-time controllers

A Temporal Framework for Hypergame Analysis of Cyber Physical Systems in Contested Environments

Game theory is used to model conflicts between one or more players over resources. It offers players a way to reason, allowing rationale for selecting strategies that avoid the worst outcome. Game theory lacks the ability to incorporate advantages one player may have over another player. A meta-game, known as a hypergame, occurs when one player does not know or fully understand all the strategies of a game. Hypergame theory builds upon the utility of game theory by allowing a player to outmaneuver an opponent, thus obtaining a more preferred outcome with higher utility. Recent work in hypergame theory has focused on normal form static games that lack the ability to encode several realistic strategies. One example of this is when a player’s available actions in the future is dependent on his selection in the past. This work presents a temporal framework for hypergame models. This framework is the first application of temporal logic to hypergames and provides a more flexible modeling for domain experts. With this new framework for hypergames, the concepts of trust, distrust, mistrust, and deception are formalized. While past literature references deception in hypergame research, this work is the first to formalize the definition for hypergames. As a demonstration of the new temporal framework for hypergames, it is applied to classical game theoretical examples, as well as a complex supervisory control and data acquisition (SCADA) network temporal hypergame. The SCADA network is an example includes actions that have a temporal dependency, where a choice in the first round affects what decisions can be made in the later round of the game. The demonstration results show that the framework is a realistic and flexible modeling method for a variety of applications

The Expressive Power, Satisfiability and Path Checking Problems of MTL and TPTL over Non-Monotonic Data Words

Recently, verification and analysis of data words have gained a lot of interest. Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are two extensions of Linear time temporal logic (LTL). In MTL, the temporal operator are indexed by a constraint interval. TPTL is a more powerful logic that is equipped with a freeze formalism. It uses register variables, which can be set to the current data value and later these register variables can be compared with the current data value. For monotonic data words, Alur and Henzinger proved that MTL and TPTL are equally expressive and the satisfiability problem is decidable. We study the expressive power, satisfiability problems and path checking problems for MLT and TPTL over all data words. We introduce Ehrenfeucht-Fraisse games for MTL and TPTL. Using the EF-game for MTL, we show that TPTL is strictly more expressive than MTL. Furthermore, we show that the MTL definability problem that whether a TPTL-formula is definable in MTL is not decidable. When restricting the number of register variables, we are able to show that TPTL with two register variables is strictly more expressive than TPTL with one register variable. For the satisfiability problem, we show that for MTL, the unary fragment of MTL and the pure fragment of MTL, SAT is not decidable. We prove the undecidability by reductions from the recurrent state problem and halting problem of two-counter machines. For the positive fragments of MTL and TPTL, we show that a positive formula is satisfiable if and only it is satisfied by a finite data word. Finitary SAT and infinitary SAT coincide for positive MTL and positive TPTL. Both of them are r.e.-complete. For existential TPTL and existential MTL, we show that SAT is NP-complete. We also investigate the complexity of path checking problems for TPTL and MTL over data words. These data words can be either finite or infinite periodic. For periodic words without data values, the complexity of LTL model checking belongs to the class AC^1(LogDCFL). For finite monotonic data words, the same complexity bound has been shown for MTL by Bundala and Ouaknine. We show that path checking for TPTL is PSPACE-complete, and for MTL is P-complete. If the number of register variables allowed is restricted, we obtain path checking for TPTL with only one register variable is P-complete over both infinite and finite data words; for TPTL with two register variables is PSPACE-complete over infinite data words. If the encoding of constraint numbers of the input TPTL-formula is in unary notation, we show that path checking for TPTL with a constant number of variables is P-complete over infinite unary encoded data words. Since the infinite data word produced by a deterministic one-counter machine is periodic, we can transfer all complexity results for the infinite periodic case to model checking over deterministic one-counter machines