1,029 research outputs found
The Complexity of Computing Optimal Assignments of Generalized Propositional Formulae
We consider the problems of finding the lexicographically minimal (or
maximal) satisfying assignment of propositional formulae for different
restricted formula classes. It turns out that for each class from our
framework, the above problem is either polynomial time solvable or complete for
OptP. We also consider the problem of deciding if in the optimal assignment the
largest variable gets value 1. We show that this problem is either in P or P^NP
complete.Comment: 17 pages, 1 figur
Taming Numbers and Durations in the Model Checking Integrated Planning System
The Model Checking Integrated Planning System (MIPS) is a temporal least
commitment heuristic search planner based on a flexible object-oriented
workbench architecture. Its design clearly separates explicit and symbolic
directed exploration algorithms from the set of on-line and off-line computed
estimates and associated data structures. MIPS has shown distinguished
performance in the last two international planning competitions. In the last
event the description language was extended from pure propositional planning to
include numerical state variables, action durations, and plan quality objective
functions. Plans were no longer sequences of actions but time-stamped
schedules. As a participant of the fully automated track of the competition,
MIPS has proven to be a general system; in each track and every benchmark
domain it efficiently computed plans of remarkable quality. This article
introduces and analyzes the most important algorithmic novelties that were
necessary to tackle the new layers of expressiveness in the benchmark problems
and to achieve a high level of performance. The extensions include critical
path analysis of sequentially generated plans to generate corresponding optimal
parallel plans. The linear time algorithm to compute the parallel plan bypasses
known NP hardness results for partial ordering by scheduling plans with respect
to the set of actions and the imposed precedence relations. The efficiency of
this algorithm also allows us to improve the exploration guidance: for each
encountered planning state the corresponding approximate sequential plan is
scheduled. One major strength of MIPS is its static analysis phase that grounds
and simplifies parameterized predicates, functions and operators, that infers
knowledge to minimize the state description length, and that detects domain
object symmetries. The latter aspect is analyzed in detail. MIPS has been
developed to serve as a complete and optimal state space planner, with
admissible estimates, exploration engines and branching cuts. In the
competition version, however, certain performance compromises had to be made,
including floating point arithmetic, weighted heuristic search exploration
according to an inadmissible estimate and parameterized optimization
Applications of Finite Model Theory: Optimisation Problems, Hybrid Modal Logics and Games.
There exists an interesting relationships between two seemingly distinct fields: logic from the field of Model Theory, which deals with the truth of statements about discrete structures; and Computational Complexity, which deals with the classification of problems by how much of a particular computer resource is required in order to compute a solution. This relationship is known as Descriptive Complexity and it is the primary application of the tools from Model Theory when they are restricted to the finite; this restriction is commonly called Finite Model Theory.
In this thesis, we investigate the extension of the results of Descriptive Complexity from classes of decision problems to classes of optimisation problems. When dealing with decision problems the natural mapping from true and false in logic to yes and no instances of a problem is used but when dealing with optimisation problems, other features of a logic need to be used. We investigate what these features are and provide results in the form of logical frameworks that can be used for describing optimisation problems in particular classes, building on the existing research into this area.
Another application of Finite Model Theory that this thesis investigates is the relative expressiveness of various fragments of an extension of modal logic called hybrid modal logic. This is achieved through taking the Ehrenfeucht-Fraïssé game from Model Theory and modifying it so that it can be applied to hybrid modal logic. Then, by developing winning strategies for the players in the game, results are obtained that show strict hierarchies of expressiveness for fragments of hybrid modal logic that are generated by varying the quantifier depth and the number of proposition and nominal symbols available
A multi-paradigm language for reactive synthesis
This paper proposes a language for describing reactive synthesis problems
that integrates imperative and declarative elements. The semantics is defined
in terms of two-player turn-based infinite games with full information.
Currently, synthesis tools accept linear temporal logic (LTL) as input, but
this description is less structured and does not facilitate the expression of
sequential constraints. This motivates the use of a structured programming
language to specify synthesis problems. Transition systems and guarded commands
serve as imperative constructs, expressed in a syntax based on that of the
modeling language Promela. The syntax allows defining which player controls
data and control flow, and separating a program into assumptions and
guarantees. These notions are necessary for input to game solvers. The
integration of imperative and declarative paradigms allows using the paradigm
that is most appropriate for expressing each requirement. The declarative part
is expressed in the LTL fragment of generalized reactivity(1), which admits
efficient synthesis algorithms, extended with past LTL. The implementation
translates Promela to input for the Slugs synthesizer and is written in Python.
The AMBA AHB bus case study is revisited and synthesized efficiently,
identifying the need to reorder binary decision diagrams during strategy
construction, in order to prevent the exponential blowup observed in previous
work.Comment: In Proceedings SYNT 2015, arXiv:1602.0078
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