3,326 research outputs found
LTLf and LDLf Synthesis under Partial Observability
In this paper, we study synthesis under partial observability for logical specifications over finite traces expressed in LTLf/LDLf. This form of synthesis can be seen as a generalization of planning under partial observability in nondeterministic domains, which is known to be 2EXPTIME-complete. We start by showing that the usual "belief-state construction" used in planning under partial observability works also for general LTLf/LDLf synthesis, though with a jump in computational complexity from 2EXPTIME to 3EXPTIME. Then we show that the belief-state construction can be avoided in favor of a direct automata construction which exploits projection to hide unobservable propositions. This allow us to prove that the problem remains 2EXPTIME-complete. The new synthesis technique proposed is effective and readily implementable
A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time
Interval Temporal Logic (ITL) is an established temporal formalism for
reasoning about time periods. For over 25 years, it has been applied in a
number of ways and several ITL variants, axiom systems and tools have been
investigated. We solve the longstanding open problem of finding a complete
axiom system for basic quantifier-free propositional ITL (PITL) with infinite
time for analysing nonterminating computational systems. Our completeness proof
uses a reduction to completeness for PITL with finite time and conventional
propositional linear-time temporal logic. Unlike completeness proofs of equally
expressive logics with nonelementary computational complexity, our semantic
approach does not use tableaux, subformula closures or explicit deductions
involving encodings of omega automata and nontrivial techniques for
complementing them. We believe that our result also provides evidence of the
naturalness of interval-based reasoning
Completeness of Flat Coalgebraic Fixpoint Logics
Modal fixpoint logics traditionally play a central role in computer science,
in particular in artificial intelligence and concurrency. The mu-calculus and
its relatives are among the most expressive logics of this type. However,
popular fixpoint logics tend to trade expressivity for simplicity and
readability, and in fact often live within the single variable fragment of the
mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL,
and the logic of common knowledge. Extending this notion to the generic
semantic framework of coalgebraic logic enables covering a wide range of logics
beyond the standard mu-calculus including, e.g., flat fragments of the graded
mu-calculus and the alternating-time mu-calculus (such as alternating-time
temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We
give a generic proof of completeness of the Kozen-Park axiomatization for such
flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on
Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer
Science, Springer, 2010, pp. 524-53
It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"
Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which finite-state processes exchange messages through unbounded FIFO channels. We study the first-order logic of MSCs, featuring Lamport\u27s happened-before relation. We introduce a star-free version of propositional dynamic logic (PDL) with loop and converse. Our main results state that (i) every first-order sentence can be transformed into an equivalent star-free PDL sentence (and conversely), and (ii) every star-free PDL sentence can be translated into an equivalent CFM. This answers an open question and settles the exact relation between CFMs and fragments of monadic second-order logic. As a byproduct, we show that first-order logic over MSCs has the three-variable property
Verification of Hierarchical Artifact Systems
Data-driven workflows, of which IBM's Business Artifacts are a prime
exponent, have been successfully deployed in practice, adopted in industrial
standards, and have spawned a rich body of research in academia, focused
primarily on static analysis. The present work represents a significant advance
on the problem of artifact verification, by considering a much richer and more
realistic model than in previous work, incorporating core elements of IBM's
successful Guard-Stage-Milestone model. In particular, the model features task
hierarchy, concurrency, and richer artifact data. It also allows database key
and foreign key dependencies, as well as arithmetic constraints. The results
show decidability of verification and establish its complexity, making use of
novel techniques including a hierarchy of Vector Addition Systems and a variant
of quantifier elimination tailored to our context.Comment: Full version of the accepted PODS pape
The Krohn-Rhodes Logics
We present a new family of modal temporal logics of the past, obtained by
extending Past LTL with a rich set of temporal operators based on the theory by
Krohn and Rhodes for automata cascades. The theory says that every automaton
can be expressed as a cascade of some basic automata called prime automata.
They are the building blocks of all automata, analogously to prime numbers
being the building blocks of all natural numbers. We show that Past LTL
corresponds to cascades of one kind of prime automata called flip-flops. In
particular, the temporal operators of Past LTL are captured by flip-flops, and
they cannot capture any other prime automaton, confining the expressivity
within the star-free regular languages. We propose novel temporal operators
that can capture other prime automata, and hence extend the expressivity of
Past LTL. Such operators are infinitely-many, and they yield an infinite number
of logics capturing an infinite number of distinct fragments of the regular
languages. The result is a yet unexplored landscape of extensions of Past LTL,
that we call Krohn-Rhodes Logics, each of them with the potential of matching
the expressivity required by specific applications
IST Austria Technical Report
We consider the distributed synthesis problem fortemporal logic specifications. Traditionally, the problem has been studied for LTL, and the previous results show that the problem is decidable iff there is no information fork in the architecture. We consider the problem for fragments of LTLand our main results are as follows: (1) We show that the problem is undecidable for architectures with information forks even for the fragment of LTL with temporal operators restricted to next and eventually. (2) For specifications restricted to globally along with non-nested next operators, we establish decidability (in EXPSPACE) for star architectures where the processes receive disjoint inputs, whereas we establish undecidability for architectures containing an information fork-meet structure. (3)Finally, we consider LTL without the next operator, and establish decidability (NEXPTIME-complete) for all architectures for a fragment that consists of a set of safety assumptions, and a set of guarantees where each guarantee is a safety, reachability, or liveness condition
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