18 research outputs found
Validity and Entailment in Modal and Propositional Dependence Logics
The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal dependence logic. Thus far, however, the validity and entailment properties of these logics have remained uncharacterised to a great extent. This paper establishes a complete classification of the complexity of validity and entailment in modal and propositional dependence logics. In particular, we address the question of the complexity of validity in modal dependence logic. By showing that it is NEXPTIME-complete we refute an earlier conjecture proposing a higher complexity for the problem
The Almost Equivalence by Asymptotic Probabilities for Regular Languages and Its Computational Complexities
We introduce p-equivalence by asymptotic probabilities, which is a weak
almost-equivalence based on zero-one laws in finite model theory. In this
paper, we consider the computational complexities of p-equivalence problems for
regular languages and provide the following details. First, we give an
robustness of p-equivalence and a logical characterization for p-equivalence.
The characterization is useful to generate some algorithms for p-equivalence
problems by coupling with standard results from descriptive complexity. Second,
we give the computational complexities for the p-equivalence problems by the
logical characterization. The computational complexities are the same as for
the (fully) equivalence problems. Finally, we apply the proofs for
p-equivalence to some generalized equivalences.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
The Adversarial Stackelberg Value in Quantitative Games
In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but ?-optimal strategies exist. We show how to compute this value and prove that the associated threshold problem is in NP. For the discounted sum payoff function, we draw a link with the target discounted sum problem which explains why the problem is difficult to solve for this payoff function. We also provide solutions to related gap problems
Fragility and Robustness in Mean-Payoff Adversarial Stackelberg Games
Two-player mean-payoff Stackelberg games are nonzero-sum infinite duration games played on a bi-weighted graph by Leader (Player 0) and Follower (Player 1). Such games are played sequentially: first, Leader announces her strategy, second, Follower chooses his best-response. If we cannot impose which best-response is chosen by Follower, we say that Follower, though strategic, is adversarial towards Leader. The maximal value that Leader can get in this nonzero-sum game is called the adversarial Stackelberg value (ASV) of the game.
We study the robustness of strategies for Leader in these games against two types of deviations: (i) Modeling imprecision - the weights on the edges of the game arena may not be exactly correct, they may be delta-away from the right one. (ii) Sub-optimal response - Follower may play epsilon-optimal best-responses instead of perfect best-responses. First, we show that if the game is zero-sum then robustness is guaranteed while in the nonzero-sum case, optimal strategies for ASV are fragile. Second, we provide a solution concept to obtain strategies for Leader that are robust to both modeling imprecision, and as well as to the epsilon-optimal responses of Follower, and study several properties and algorithmic problems related to this solution concept
The Adversarial Stackelberg Value in Quantitative Games
In this paper, we study the notion of adversarial Stackelberg value for
two-player non-zero sum games played on bi-weighted graphs with the mean-payoff
and the discounted sum functions. The adversarial Stackelberg value of Player 0
is the largest value that Player 0 can obtain when announcing her strategy to
Player 1 which in turn responds with any of his best response. For the
mean-payoff function, we show that the adversarial Stackelberg value is not
always achievable but epsilon-optimal strategies exist. We show how to compute
this value and prove that the associated threshold problem is in NP. For the
discounted sum payoff function, we draw a link with the target discounted sum
problem which explains why the problem is difficult to solve for this payoff
function. We also provide solutions to related gap problems.Comment: long version of an ICALP'20 pape
On elementary logics for quantitative dependencies
We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under the Boolean negation. Our logics employ new probabilistic atoms that resemble so-called extended atoms from the team semantics literature. We also define counterparts of our logics over metafinite structures and show that all of our logics can be translated into functional fixed point logic implying a polynomial time upper bound for data complexity with respect to BSS-computations.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe
Complexity Thresholds in Inclusion Logic
Logics with team semantics provide alternative means for logical
characterization of complexity classes. Both dependence and independence logic
are known to capture non-deterministic polynomial time, and the frontiers of
tractability in these logics are relatively well understood. Inclusion logic is
similar to these team-based logical formalisms with the exception that it
corresponds to deterministic polynomial time in ordered models. In this article
we examine connections between syntactical fragments of inclusion logic and
different complexity classes in terms of two computational problems: maximal
subteam membership and the model checking problem for a fixed inclusion logic
formula. We show that very simple quantifier-free formulae with one or two
inclusion atoms generate instances of these problems that are complete for
(non-deterministic) logarithmic space and polynomial time. Furthermore, we
present a fragment of inclusion logic that captures non-deterministic
logarithmic space in ordered models