1,066 research outputs found
A Theory of Sampling for Continuous-time Metric Temporal Logic
This paper revisits the classical notion of sampling in the setting of
real-time temporal logics for the modeling and analysis of systems. The
relationship between the satisfiability of Metric Temporal Logic (MTL) formulas
over continuous-time models and over discrete-time models is studied. It is
shown to what extent discrete-time sequences obtained by sampling
continuous-time signals capture the semantics of MTL formulas over the two time
domains. The main results apply to "flat" formulas that do not nest temporal
operators and can be applied to the problem of reducing the verification
problem for MTL over continuous-time models to the same problem over
discrete-time, resulting in an automated partial practically-efficient
discretization technique.Comment: Revised version, 43 pages
Specific-to-General Learning for Temporal Events with Application to Learning Event Definitions from Video
We develop, analyze, and evaluate a novel, supervised, specific-to-general
learner for a simple temporal logic and use the resulting algorithm to learn
visual event definitions from video sequences. First, we introduce a simple,
propositional, temporal, event-description language called AMA that is
sufficiently expressive to represent many events yet sufficiently restrictive
to support learning. We then give algorithms, along with lower and upper
complexity bounds, for the subsumption and generalization problems for AMA
formulas. We present a positive-examples--only specific-to-general learning
method based on these algorithms. We also present a polynomial-time--computable
``syntactic'' subsumption test that implies semantic subsumption without being
equivalent to it. A generalization algorithm based on syntactic subsumption can
be used in place of semantic generalization to improve the asymptotic
complexity of the resulting learning algorithm. Finally, we apply this
algorithm to the task of learning relational event definitions from video and
show that it yields definitions that are competitive with hand-coded ones
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
Exponential separations using guarded extension variables
We study the complexity of proof systems augmenting resolution with inference
rules that allow, given a formula in conjunctive normal form, deriving
clauses that are not necessarily logically implied by but whose
addition to preserves satisfiability. When the derived clauses are
allowed to introduce variables not occurring in , the systems we
consider become equivalent to extended resolution. We are concerned with the
versions of these systems without new variables. They are called BC,
RAT, SBC, and GER, denoting respectively blocked clauses,
resolution asymmetric tautologies, set-blocked clauses, and generalized
extended resolution. Each of these systems formalizes some restricted version
of the ability to make assumptions that hold "without loss of generality,"
which is commonly used informally to simplify or shorten proofs.
Except for SBC, these systems are known to be exponentially weaker than
extended resolution. They are, however, all equivalent to it under a relaxed
notion of simulation that allows the translation of the formula along with the
proof when moving between proof systems. By taking advantage of this fact, we
construct formulas that separate RAT from GER and vice versa. With
the same strategy, we also separate SBC from RAT. Additionally, we
give polynomial-size SBC proofs of the pigeonhole principle, which
separates SBC from GER by a previously known lower bound. These
results also separate the three systems from BC since they all simulate
it. We thus give an almost complete picture of their relative strengths
Even shorter proofs without new variables
Proof formats for SAT solvers have diversified over the last decade, enabling
new features such as extended resolution-like capabilities, very general
extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning.
Interference-based methods have been proven effective, and some theoretical
work has been undertaken to better explain their limits and semantics. In this
work, we combine the subsumption redundancy notion from (Buss, Thapen 2019) and
the overwrite logic framework from (Rebola-Pardo, Suda 2018). Natural
generalizations then become apparent, enabling even shorter proofs of the
pigeonhole principle (compared to those from (Heule, Kiesl, Biere 2017)) and
smaller unsatisfiable core generation.Comment: 21 page
Advanced Symbolic Analysis Tools for Fault-Tolerant Integrated Distributed Systems
The project aims to develop advanced model-checking algorithms and tools to automate the verification of fault-tolerant distributed systems for avionics. We present a new method called Property-Directed K-Induction (PD-KIND) for synthesizing K-inductive invariants of state-transition systems. PD-KIND builds upon Satifiability Modulo Theories (SMT) to generalize Bradley's IC3 method and its variants. This method is implemented in a new tool called SALLY. Case studies show that PD-KIND can automatically verify fault-tolerant algorithms under a variety of fault models and that SALLY is competitive with other SMT-based model checkers
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