201 research outputs found
Flow Logic
Flow networks have attracted a lot of research in computer science. Indeed,
many questions in numerous application areas can be reduced to questions about
flow networks. Many of these applications would benefit from a framework in
which one can formally reason about properties of flow networks that go beyond
their maximal flow. We introduce Flow Logics: modal logics that treat flow
functions as explicit first-order objects and enable the specification of rich
properties of flow networks. The syntax of our logic BFL* (Branching Flow
Logic) is similar to the syntax of the temporal logic CTL*, except that atomic
assertions may be flow propositions, like or , for
, which refer to the value of the flow in a vertex, and
that first-order quantification can be applied both to paths and to flow
functions. We present an exhaustive study of the theoretical and practical
aspects of BFL*, as well as extensions and fragments of it. Our extensions
include flow quantifications that range over non-integral flow functions or
over maximal flow functions, path quantification that ranges over paths along
which non-zero flow travels, past operators, and first-order quantification of
flow values. We focus on the model-checking problem and show that it is
PSPACE-complete, as it is for CTL*. Handling of flow quantifiers, however,
increases the complexity in terms of the network to , even
for the LFL and BFL fragments, which are the flow-counterparts of LTL and CTL.
We are still able to point to a useful fragment of BFL* for which the
model-checking problem can be solved in polynomial time. Finally, we introduce
and study the query-checking problem for BFL*, where under-specified BFL*
formulas are used for network exploration
Coverage and Vacuity in Network Formation Games
The frameworks of coverage and vacuity in formal verification analyze the effect of mutations applied to systems or their specifications. We adopt these notions to network formation games, analyzing the effect of a change in the cost of a resource. We consider two measures to be affected: the cost of the Social Optimum and extremums of costs of Nash Equilibria. Our results offer a formal framework to the effect of mutations in network formation games and include a complexity analysis of related decision problems. They also tighten the relation between algorithmic game theory and formal verification, suggesting refined definitions of coverage and vacuity for the latter
Minimizing Expected Cost Under Hard Boolean Constraints, with Applications to Quantitative Synthesis
In Boolean synthesis, we are given an LTL specification, and the goal is to
construct a transducer that realizes it against an adversarial environment.
Often, a specification contains both Boolean requirements that should be
satisfied against an adversarial environment, and multi-valued components that
refer to the quality of the satisfaction and whose expected cost we would like
to minimize with respect to a probabilistic environment.
In this work we study, for the first time, mean-payoff games in which the
system aims at minimizing the expected cost against a probabilistic
environment, while surely satisfying an -regular condition against an
adversarial environment. We consider the case the -regular condition is
given as a parity objective or by an LTL formula. We show that in general,
optimal strategies need not exist, and moreover, the limit value cannot be
approximated by finite-memory strategies. We thus focus on computing the
limit-value, and give tight complexity bounds for synthesizing
-optimal strategies for both finite-memory and infinite-memory
strategies.
We show that our game naturally arises in various contexts of synthesis with
Boolean and multi-valued objectives. Beyond direct applications, in synthesis
with costs and rewards to certain behaviors, it allows us to compute the
minimal sensing cost of -regular specifications -- a measure of quality
in which we look for a transducer that minimizes the expected number of signals
that are read from the input
Eulerian Paths with Regular Constraints
Labeled graphs, in which edges are labeled by letters from some alphabet Sigma, are extensively used to model many types of
relations associated with actions, costs, owners, or other
properties. Each path in a labeled graph induces a word in Sigma^*
-- the one obtained by concatenating the letters along the edges in
the path. Classical graph-theory problems give rise to new problems
that take these words into account. We introduce and study the
constrained Eulerian path problem. The input to the problem is a
Sigma-labeled graph G and a specification L subseteq Sigma^*.
The goal is to find an Eulerian path in G that satisfies L. We
consider several classes of the problem, defined by the classes of G
and L. We focus on the case L is regular and show that while the
problem is in general NP-complete, even for very simple graphs and
specifications, there are classes that can be solved efficiently. Our
results extend work on Eulerian paths with edge-order constraints. We
also study the constrained Chinese postman problem, where
edges have costs and the goal is to find a cheapest path that contains
each edge at least once and satisfies the specification. Finally, we
define and study the Eulerian language of a graph, namely the
set of words along its Eulerian paths
High-Quality Synthesis Against Stochastic Environments
In the classical synthesis problem, we are given a linear temporal logic (LTL) formula psi over sets of input and output signals, and we synthesize a transducer that realizes psi: with every sequence of input signals, the transducer associates a sequence of output signals so that the generated computation satisfies psi. One weakness of automated synthesis in practice is that it pays no attention to the quality of the synthesized system. Indeed, the classical setting is Boolean: a computation satisfies a specification or does not satisfy it. Accordingly, while the synthesized system is correct, there is no guarantee about its quality. In recent years, researchers have considered extensions of the classical Boolean setting to a quantitative one. The logic FLTL is a multi-valued logic that augments LTL with quality operators. The satisfaction value of an FLTL formula is a real value in [0,1], where the higher the value is, the higher is the quality in which the computation satisfies the specification.
Decision problems for LTL become search or optimization problems for FLTL. In particular, in the synthesis problem, the goal is to generate a transducer that satisfies the specification in the highest possible quality. Previous work considered the worst-case setting, where the goal is to maximize the quality of the computation with the minimal quality. We introduce and solve the stochastic setting, where the goal is to generate a transducer that maximizes the expected quality of a computation, subject to a given distribution of the input signals. Thus, rather than being hostile, the environment is assumed to be probabilistic, which corresponds to many realistic settings. We show that the problem is 2EXPTIME-complete, like classical LTL synthesis. The complexity stays 2EXPTIME also in two extensions we consider: one that maximizes the expected quality while guaranteeing that the minimal quality is, with probability 1, above a given threshold, and one that allows assumptions on the environment
The Unfortunate-Flow Problem
In the traditional maximum-flow problem, the goal is to transfer maximum flow in a network by directing, in each vertex in the network, incoming flow into outgoing edges. The problem is one of the most fundamental problems in TCS, with application in numerous domains. The fact a maximal-flow algorithm directs the flow in all the vertices of the network corresponds to a setting in which the authority has control in all vertices. Many applications in which the maximal-flow problem is applied involve an adversarial setting, where the authority does not have such a control.
We introduce and study the unfortunate flow problem, which studies the flow that is guaranteed to reach the target when the edges that leave the source are saturated, yet the most unfortunate decisions are taken in the vertices. When the incoming flow to a vertex is greater than the outgoing capacity, flow is lost. The problem models evacuation scenarios where traffic is stuck due to jams in junctions and communication networks where packets are dropped in overloaded routers.
We study the theoretical properties of unfortunate flows, show that the unfortunate-flow problem is co-NP-complete and point to polynomial fragments. We introduce and study interesting variants of the problem: integral unfortunate flow, where the flow along edges must be integral, controlled unfortunate flow, where the edges from the source need not be saturated and may be controlled, and no-loss controlled unfortunate flow, where the controlled flow must not be lost
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