876 research outputs found
ATLsc with partial observation
Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful
formalism for expressing properties of multi-agent systems: it extends CTL with
strategy quantifiers, offering a convenient way of expressing both
collaboration and antagonism between several agents. Incomplete observation of
the state space is a desirable feature in such a framework, but it quickly
leads to undecidable verification problems. In this paper, we prove that
uniform incomplete observation (where all players have the same observation)
preserves decidability of the model-checking problem, even for very expressive
logics such as ATLsc.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Real Computational Universality: The Word Problem for a class of groups with infinite presentation
The word problem for discrete groups is well-known to be undecidable by a
Turing Machine; more precisely, it is reducible both to and from and thus
equivalent to the discrete Halting Problem.
The present work introduces and studies a real extension of the word problem
for a certain class of groups which are presented as quotient groups of a free
group and a normal subgroup. Most important, the free group will be generated
by an uncountable set of generators with index running over certain sets of
real numbers. This allows to include many mathematically important groups which
are not captured in the framework of the classical word problem.
Our contribution extends computational group theory from the discrete to the
Blum-Shub-Smale (BSS) model of real number computation. We believe this to be
an interesting step towards applying BSS theory, in addition to semi-algebraic
geometry, also to further areas of mathematics.
The main result establishes the word problem for such groups to be not only
semi-decidable (and thus reducible FROM) but also reducible TO the Halting
Problem for such machines. It thus provides the first non-trivial example of a
problem COMPLETE, that is, computationally universal for this model.Comment: corrected Section 4.
What's Decidable About Sequences?
We present a first-order theory of sequences with integer elements,
Presburger arithmetic, and regular constraints, which can model significant
properties of data structures such as arrays and lists. We give a decision
procedure for the quantifier-free fragment, based on an encoding into the
first-order theory of concatenation; the procedure has PSPACE complexity. The
quantifier-free fragment of the theory of sequences can express properties such
as sortedness and injectivity, as well as Boolean combinations of periodic and
arithmetic facts relating the elements of the sequence and their positions
(e.g., "for all even i's, the element at position i has value i+3 or 2i"). The
resulting expressive power is orthogonal to that of the most expressive
decidable logics for arrays. Some examples demonstrate that the fragment is
also suitable to reason about sequence-manipulating programs within the
standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl
Plan Synthesis for Knowledge and Action Bases
We study plan synthesis for a variant of Knowledge and Action Bases (KABs), a rich, dynamic framework, where states are description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that possibly introduce new objects from an infinite domain. We show that plan existence over KABs is undecidable even under severe restrictions. We then focus on state-bounded KABs, a class for which plan existence is decidable, and provide sound and complete plan synthesis algorithms, which combine techniques based on standard planning, DL query answering, and finite-state abstraction. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning
Infinite games with finite knowledge gaps
Infinite games where several players seek to coordinate under imperfect
information are deemed to be undecidable, unless the information is
hierarchically ordered among the players.
We identify a class of games for which joint winning strategies can be
constructed effectively without restricting the direction of information flow.
Instead, our condition requires that the players attain common knowledge about
the actual state of the game over and over again along every play.
We show that it is decidable whether a given game satisfies the condition,
and prove tight complexity bounds for the strategy synthesis problem under
-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio
Synthesizing and executing plans in Knowledge and Action Bases
We study plan synthesis for a variant of Knowledge and Action Bases (KABs). KABs have been recently introduced as a rich, dynamic framework where states are full-fledged description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that can introduce new objects from an infinite domain. We show that, in general, plan existence over KABs is undecidable even under severe restrictions. We then focus on the class of state-bounded KABs, for which plan existence is decidable, and we provide sound and complete plan synthesis algorithms, through a novel combination of techniques based on standard planning, DL query answering, and finite-state abstractions. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning. © 2016, CEUR-WS. All rights reserved
Automated Generation of Unit Tests from UML Activity Diagrams using the AMPL Interface for Constraint Solvers
I, Felix Kurth, declare that I have authored this thesis independently, that I have not used other than the declared sources / resources, and that I have explicitly marked all material which has been quoted either literally or by content from the used sources. Neither this thesis nor any other similar work has been previously submitted to any examination board
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