1,414 research outputs found
Optimal state reductions of automata with partially specified behaviors
Nondeterministic finite automata with don't care states, namely states which neither accept nor reject, are considered. A characterization of deterministic automata compatible with such a device is obtained. Furthermore, an optimal state bound for the smallest compatible deterministic automata is provided. It is proved that the problem of minimizing deterministic don't care automata is NP-complete and PSPACE-hard in the nondeterministic case. The restriction to the unary case is also considered
Optimal State Reductions of Automata with Partially Specified Behaviors
Nondeterministic finite automata with don't care states, namely states which neither accept nor reject, are considered. A characterization of deterministic automata compatible with such a device is obtained. Furthermore, an optimal state bound for the smallest compatible deterministic automata is provided. Finally, it is proved that the problem of minimizing nondeterministic and deterministic don't care automata is NP-complete
Linear Temporal Logic-based Mission Planning
In this paper, we describe the Linear Temporal
Logic-based reactive motion planning. We address the problem of
motion planning for mobile robots, wherein the goal specification
of planning is given in complex environments. The desired task
specification may consist of complex behaviors of the robot,
including specifications for environment constraints, need of task
optimality, obstacle avoidance, rescue specifications, surveillance
specifications, safety specifications, etc. We use Linear Temporal
Logic to give a representation for such complex task specification
and constraints. The specifications are used by a verification engine
to judge the feasibility and suitability of plans. The planner gives a
motion strategy as output. Finally a controller is used to generate
the desired trajectory to achieve such a goal. The approach is
tested using simulations on the LTLMoP mission planning tool,
operating over the Robot Operating System. Simulation results
generated using high level planners and low level controllers work
simultaneously for mission planning and controlling the physical
behavior of the robot
Conditionally Optimal Algorithms for Generalized B\"uchi Games
Games on graphs provide the appropriate framework to study several central
problems in computer science, such as the verification and synthesis of
reactive systems. One of the most basic objectives for games on graphs is the
liveness (or B\"uchi) objective that given a target set of vertices requires
that some vertex in the target set is visited infinitely often. We study
generalized B\"uchi objectives (i.e., conjunction of liveness objectives), and
implications between two generalized B\"uchi objectives (known as GR(1)
objectives), that arise in numerous applications in computer-aided
verification. We present improved algorithms and conditional super-linear lower
bounds based on widely believed assumptions about the complexity of (A1)
combinatorial Boolean matrix multiplication and (A2) CNF-SAT. We consider graph
games with vertices, edges, and generalized B\"uchi objectives with
conjunctions. First, we present an algorithm with running time , improving the previously known and worst-case bounds. Our algorithm is optimal for dense graphs under (A1).
Second, we show that the basic algorithm for the problem is optimal for sparse
graphs when the target sets have constant size under (A2). Finally, we consider
GR(1) objectives, with conjunctions in the antecedent and
conjunctions in the consequent, and present an -time algorithm, improving the previously known -time algorithm for
Qualitative Analysis of Partially-observable Markov Decision Processes
We study observation-based strategies for partially-observable Markov
decision processes (POMDPs) with omega-regular objectives. An observation-based
strategy relies on partial information about the history of a play, namely, on
the past sequence of observations. We consider the qualitative analysis
problem: given a POMDP with an omega-regular objective, whether there is an
observation-based strategy to achieve the objective with probability~1
(almost-sure winning), or with positive probability (positive winning). Our
main results are twofold. First, we present a complete picture of the
computational complexity of the qualitative analysis of POMDP s with parity
objectives (a canonical form to express omega-regular objectives) and its
subclasses. Our contribution consists in establishing several upper and lower
bounds that were not known in literature. Second, we present optimal bounds
(matching upper and lower bounds) on the memory required by pure and randomized
observation-based strategies for the qualitative analysis of POMDP s with
parity objectives and its subclasses
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