9,626 research outputs found
A Cyclic Proof System for Full Computation Tree Logic
Full Computation Tree Logic, commonly denoted CTL*, is the extension of Linear Temporal Logic LTL by path quantification for reasoning about branching time. In contrast to traditional Computation Tree Logic CTL, the path quantifiers are not bound to specific linear modalities, resulting in a more expressive language. We present a sound and complete hypersequent calculus for CTL*. The proof system is cyclic in the sense that proofs are finite derivation trees with back-edges. A syntactic success condition on non-axiomatic leaves guarantees soundness. Completeness is established by relating cyclic proofs to a natural ill-founded sequent calculus for the logic
Hybrid Branching-Time Logics
Hybrid branching-time logics are introduced as extensions of CTL-like logics
with state variables and the downarrow-binder. Following recent work in the
linear framework, only logics with a single variable are considered. The
expressive power and the complexity of satisfiability of the resulting logics
is investigated.
As main result, the satisfiability problem for the hybrid versions of several
branching-time logics is proved to be 2EXPTIME-complete. These branching-time
logics range from strict fragments of CTL to extensions of CTL that can talk
about the past and express fairness-properties. The complexity gap relative to
CTL is explained by a corresponding succinctness result.
To prove the upper bound, the automata-theoretic approach to branching-time
logics is extended to hybrid logics, showing that non-emptiness of alternating
one-pebble Buchi tree automata is 2EXPTIME-complete.Comment: An extended abstract of this paper was presented at the International
Workshop on Hybrid Logics (HyLo 2007
FINITE H-DIMENSION DOES NOT IMPLY EXPRESSIVE COMPLETENESS
Accepted versio
First-Order and Temporal Logics for Nested Words
Nested words are a structured model of execution paths in procedural
programs, reflecting their call and return nesting structure. Finite nested
words also capture the structure of parse trees and other tree-structured data,
such as XML. We provide new temporal logics for finite and infinite nested
words, which are natural extensions of LTL, and prove that these logics are
first-order expressively-complete. One of them is based on adding a "within"
modality, evaluating a formula on a subword, to a logic CaRet previously
studied in the context of verifying properties of recursive state machines
(RSMs). The other logic, NWTL, is based on the notion of a summary path that
uses both the linear and nesting structures. For NWTL we show that
satisfiability is EXPTIME-complete, and that model-checking can be done in time
polynomial in the size of the RSM model and exponential in the size of the NWTL
formula (and is also EXPTIME-complete). Finally, we prove that first-order
logic over nested words has the three-variable property, and we present a
temporal logic for nested words which is complete for the two-variable fragment
of first-order.Comment: revised and corrected version of Mar 03, 201
Model Checking Dynamic-Epistemic Spatial Logic
In this paper we focus on Dynamic Spatial Logic, the extension of Hennessy-Milner logic with the parallel operator. We develop a sound complete Hilbert-style axiomatic system for it comprehending the behavior of spatial operators in relation with dynamic/temporal ones. Underpining on a new congruence we define over the class of processes - the structural bisimulation - we prove the finite model property for this logic that provides the decidability for satisfiability, validity and model checking against process semantics. Eventualy we propose algorithms for validity, satisfiability and model checking
Two-Way Unary Temporal Logic over Trees
We consider a temporal logic EF+F^-1 for unranked, unordered finite trees.
The logic has two operators: EF\phi, which says "in some proper descendant \phi
holds", and F^-1\phi, which says "in some proper ancestor \phi holds". We
present an algorithm for deciding if a regular language of unranked finite
trees can be expressed in EF+F^-1. The algorithm uses a characterization
expressed in terms of forest algebras.Comment: 29 pages. Journal version of a LICS 07 pape
Expressiveness of the modal mu-calculus on monotone neighborhood structures
We characterize the expressive power of the modal mu-calculus on monotone
neighborhood structures, in the style of the Janin-Walukiewicz theorem for the
standard modal mu-calculus. For this purpose we consider a monadic second-order
logic for monotone neighborhood structures. Our main result shows that the
monotone modal mu-calculus corresponds exactly to the fragment of this
second-order language that is invariant for neighborhood bisimulations
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
- …