7,301 research outputs found
The Wadge Hierarchy of Deterministic Tree Languages
We provide a complete description of the Wadge hierarchy for
deterministically recognisable sets of infinite trees. In particular we give an
elementary procedure to decide if one deterministic tree language is
continuously reducible to another. This extends Wagner's results on the
hierarchy of omega-regular languages of words to the case of trees.Comment: 44 pages, 8 figures; extended abstract presented at ICALP 2006,
Venice, Italy; full version appears in LMCS special issu
Argument filterings and usable rules in higher-order rewrite systems
The static dependency pair method is a method for proving the termination of
higher-order rewrite systems a la Nipkow. It combines the dependency pair
method introduced for first-order rewrite systems with the notion of strong
computability introduced for typed lambda-calculi. Argument filterings and
usable rules are two important methods of the dependency pair framework used by
current state-of-the-art first-order automated termination provers. In this
paper, we extend the class of higher-order systems on which the static
dependency pair method can be applied. Then, we extend argument filterings and
usable rules to higher-order rewriting, hence providing the basis for a
powerful automated termination prover for higher-order rewrite systems
User's guide to SFTRAN/1100
Extensions and improvements were made to SFTRAN, a structured programming language. This language was implemented as a precompiler that translates from SFTRAN to FORTRAN. It was available to batch and conversational users of the UNIVAC 1100 computer system. The SFTRAN language and its use are described. In addition, conversational time-sharing system command subroutines were implemented that eliminated the complications of dealing with extra files and processing steps that the use of a precompiler would otherwise require. These command subroutines are reported, and their use is illustrated by examples
Rich Counter-Examples for Temporal-Epistemic Logic Model Checking
Model checking verifies that a model of a system satisfies a given property,
and otherwise produces a counter-example explaining the violation. The verified
properties are formally expressed in temporal logics. Some temporal logics,
such as CTL, are branching: they allow to express facts about the whole
computation tree of the model, rather than on each single linear computation.
This branching aspect is even more critical when dealing with multi-modal
logics, i.e. logics expressing facts about systems with several transition
relations. A prominent example is CTLK, a logic that reasons about temporal and
epistemic properties of multi-agent systems. In general, model checkers produce
linear counter-examples for failed properties, composed of a single computation
path of the model. But some branching properties are only poorly and partially
explained by a linear counter-example.
This paper proposes richer counter-example structures called tree-like
annotated counter-examples (TLACEs), for properties in Action-Restricted CTL
(ARCTL), an extension of CTL quantifying paths restricted in terms of actions
labeling transitions of the model. These counter-examples have a branching
structure that supports more complete description of property violations.
Elements of these counter-examples are annotated with parts of the property to
give a better understanding of their structure. Visualization and browsing of
these richer counter-examples become a critical issue, as the number of
branches and states can grow exponentially for deeply-nested properties.
This paper formally defines the structure of TLACEs, characterizes adequate
counter-examples w.r.t. models and failed properties, and gives a generation
algorithm for ARCTL properties. It also illustrates the approach with examples
in CTLK, using a reduction of CTLK to ARCTL. The proposed approach has been
implemented, first by extending the NuSMV model checker to generate and export
branching counter-examples, secondly by providing an interactive graphical
interface to visualize and browse them.Comment: In Proceedings IWIGP 2012, arXiv:1202.422
Multi-Scale Jacobi Method for Anderson Localization
A new KAM-style proof of Anderson localization is obtained. A sequence of
local rotations is defined, such that off-diagonal matrix elements of the
Hamiltonian are driven rapidly to zero. This leads to the first proof via
multi-scale analysis of exponential decay of the eigenfunction correlator (this
implies strong dynamical localization). The method has been used in recent work
on many-body localization [arXiv:1403.7837].Comment: 34 pages, 8 figures, clarifications and corrections for published
version; more detail in Section 4.
User's guide for SFTRAN/360
Extension and improvements made to SFTRAN, a structured-programming language are discussed. This improved language is implemented as a precompiler that translates from SFTRAN to FORTRAN. The SFTRAN language and its use are described. Time-Sharing System (TSS) command procedures were implemented that eliminate the complications of dealing with extra files and processing steps which the use of a precompiler would otherwise require. These command procedures are described and their use is illustrated by examples
A Decidable Class of Nested Iterated Schemata (extended version)
Many problems can be specified by patterns of propositional formulae
depending on a parameter, e.g. the specification of a circuit usually depends
on the number of bits of its input. We define a logic whose formulae, called
"iterated schemata", allow to express such patterns. Schemata extend
propositional logic with indexed propositions, e.g. P_i, P_i+1, P_1, and with
generalized connectives, e.g. /\i=1..n or i=1..n (called "iterations") where n
is an (unbound) integer variable called a "parameter". The expressive power of
iterated schemata is strictly greater than propositional logic: it is even out
of the scope of first-order logic. We define a proof procedure, called DPLL*,
that can prove that a schema is satisfiable for at least one value of its
parameter, in the spirit of the DPLL procedure. However the converse problem,
i.e. proving that a schema is unsatisfiable for every value of the parameter,
is undecidable so DPLL* does not terminate in general. Still, we prove that it
terminates for schemata of a syntactic subclass called "regularly nested". This
is the first non trivial class for which DPLL* is proved to terminate.
Furthermore the class of regularly nested schemata is the first decidable class
to allow nesting of iterations, i.e. to allow schemata of the form /\i=1..n
(/\j=1..n ...).Comment: 43 pages, extended version of "A Decidable Class of Nested Iterated
Schemata", submitted to IJCAR 200
Index problems for game automata
For a given regular language of infinite trees, one can ask about the minimal
number of priorities needed to recognize this language with a
non-deterministic, alternating, or weak alternating parity automaton. These
questions are known as, respectively, the non-deterministic, alternating, and
weak Rabin-Mostowski index problems. Whether they can be answered effectively
is a long-standing open problem, solved so far only for languages recognizable
by deterministic automata (the alternating variant trivializes).
We investigate a wider class of regular languages, recognizable by so-called
game automata, which can be seen as the closure of deterministic ones under
complementation and composition. Game automata are known to recognize languages
arbitrarily high in the alternating Rabin-Mostowski index hierarchy; that is,
the alternating index problem does not trivialize any more.
Our main contribution is that all three index problems are decidable for
languages recognizable by game automata. Additionally, we show that it is
decidable whether a given regular language can be recognized by a game
automaton
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