More on Descriptive Complexity of Second-Order HORN Logics

This paper concerns Gradel's question asked in 1992: whether all problems which are in PTIME and closed under substructures are definable in second-order HORN logic SO-HORN. We introduce revisions of SO-HORN and DATALOG by adding first-order universal quantifiers over the second-order atoms in the bodies of HORN clauses and DATALOG rules. We show that both logics are as expressive as FO(LFP), the least fixed point logic. We also prove that FO(LFP) can not define all of the problems that are in PTIME and closed under substructures. As a corollary, we answer Gradel's question negatively

Real-time Motion Planning For Autonomous Car in Multiple Situations Under Simulated Urban Environment

Advanced autonomous cars have revolutionary meaning for the automobile industry. While more and more companies have already started to build their own autonomous cars, no one has yet brought a practical autonomous car into the market. One key problem of their cars is lacking a reliable active real-time motion planning system for the urban environment. A real-time motion planning system makes cars can safely and stably drive under the urban environment. The final goal for this project is to design and implement a reliable real-time motion planning system to reduce accident rates in autonomous cars instead of human drivers. The real-time motion planning system includes lane-keeping, obstacle avoidance, moving car avoidance, adaptive cruise control, and accident avoidance function. In the research, EGO vehicles will be built and equipped with an image processing unit, a LIDAR, and two ultrasonic sensors to detect the environment. These environment data make it possible to implement a full control program in the real-time motion planning system. The control program will be implemented and tested in a scaled-down EGO vehicle with a scaled-down urban environment. The project has been divided into three phases: build EGO vehicles, implement the control program of the real-time motion planning system, and improve the control program by testing under the scale-down urban environment. In the first phase, each EGO vehicle will be built by an EGO vehicle chassis kit, a Raspberry Pi, a LIDAR, two ultrasonic sensors, a battery, and a power board. In the second phase, the control program of the real-time motion planning system will be implemented under the lane-keeping program in Raspberry Pi. Python is the programming language that will be used to implement the program. Lane-keeping, obstacle avoidance, moving car avoidance, adaptive cruise control functions will be built in this control program. In the last phase, testing and improvement works will be finished. Reliability tests will be designed and fulfilled. The more data grab from tests, the more stability of the real-time motion planning system can be implemented. Finally, one reliable motion planning system will be built, which will be used in normal scale EGO vehicles to reduce accident rates significantly under the urban environment.No embargoAcademic Major: Electrical and Computer Engineerin

Reasoning about Knowledge and Strategies under Hierarchical Information

Two distinct semantics have been considered for knowledge in the context of strategic reasoning, depending on whether players know each other's strategy or not. The problem of distributed synthesis for epistemic temporal specifications is known to be undecidable for the latter semantics, already on systems with hierarchical information. However, for the other, uninformed semantics, the problem is decidable on such systems. In this work we generalise this result by introducing an epistemic extension of Strategy Logic with imperfect information. The semantics of knowledge operators is uninformed, and captures agents that can change observation power when they change strategies. We solve the model-checking problem on a class of "hierarchical instances", which provides a solution to a vast class of strategic problems with epistemic temporal specifications on hierarchical systems, such as distributed synthesis or rational synthesis

A Logic with Reverse Modalities for History-preserving Bisimulations

We introduce event identifier logic (EIL) which extends Hennessy-Milner logic by the addition of (1) reverse as well as forward modalities, and (2) identifiers to keep track of events. We show that this logic corresponds to hereditary history-preserving (HH) bisimulation equivalence within a particular true-concurrency model, namely stable configuration structures. We furthermore show how natural sublogics of EIL correspond to coarser equivalences. In particular we provide logical characterisations of weak history-preserving (WH) and history-preserving (H) bisimulation. Logics corresponding to HH and H bisimulation have been given previously, but not to WH bisimulation (when autoconcurrency is allowed), as far as we are aware. We also present characteristic formulas which characterise individual structures with respect to history-preserving equivalences.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SLii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems. To establish the decidability result, we introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL* with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL* ii allows us to provide a conceptually neat reduction of SLii to QCTL*ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL*ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. The decidability result for SLii follows since the reduction maps hierarchical instances of SLii to hierarchical formulas of QCTL*ii

A New Game Equivalence and its Modal Logic

We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal bisimulation. Concretely, we propose a more finegrained notion of equality of "basic powers" which record what players can force plus what they leave to others to do, a crucial feature of interaction. This notion is closer to game-theoretic strategic form, as we explain in detail, while remaining amenable to logical analysis. We determine the properties of basic powers via a new representation theorem, find a matching "instantial neighborhood game logic", and show how our analysis can be extended to a new game algebra and dynamic game logic.Comment: In Proceedings TARK 2017, arXiv:1707.0825