58 research outputs found
Results on Alternating-Time Temporal Logics with Linear Past
We investigate the succinctness gap between two known equally-expressive and different linear-past extensions of standard CTL^* (resp., ATL^*). We establish by formal non-trivial arguments that the "memoryful" linear-past extension (the history leading to the current state is taken into account) can be exponentially more succinct than the standard "local" linear-past extension (the history leading to the current state is forgotten). As a second contribution, we consider the ATL-like fragment, denoted ATL_{lp}, of the known "memoryful" linear-past extension of ATL^{*}. We show that ATL_{lp} is strictly more expressive than ATL, and interestingly, it can be exponentially more succinct than the more expressive logic ATL^{*}. Moreover, we prove that both satisfiability and model-checking for the logic ATL_{lp} are Exptime-complete
MCMAS-SLK: A Model Checker for the Verification of Strategy Logic Specifications
We introduce MCMAS-SLK, a BDD-based model checker for the verification of
systems against specifications expressed in a novel, epistemic variant of
strategy logic. We give syntax and semantics of the specification language and
introduce a labelling algorithm for epistemic and strategy logic modalities. We
provide details of the checker which can also be used for synthesising agents'
strategies so that a specification is satisfied by the system. We evaluate the
efficiency of the implementation by discussing the results obtained for the
dining cryptographers protocol and a variant of the cake-cutting problem
Relentful Strategic Reasoning in 1 Alternating-Time Temporal Logic
Temporal logics are a well investigated formalism for the specification, verification, and synthesis of reactive systems.
Within this family, Alternating-Time Temporal Logic (ATL , for short) has been introduced as a useful generalization
of classical linear- and branching-time temporal logics, by allowing temporal operators to be indexed by coalitions of
agents. Classically, temporal logics are memoryless: once a path in the computation tree is quantified at a given node,
the computation that has led to that node is forgotten. Recently, mCTL has been defined as a memoryful variant
of CTL , where path quantification is memoryful. In the context of multi-agent planning, memoryful quantification
enables agents to “relent” and change their goals and strategies depending on their history.
In this paper, we define mATL , a memoryful extension of ATL , in which a formula is satisfied at a certain
node of a path by taking into account both the future and the past. We study the expressive power of mATL ,
its succinctness, as well as related decision problems. We also investigate the relationship between memoryful
quantification and past modalities and show their equivalence. We show that both the memoryful and the past
extensions come without any computational price; indeed, we prove that both the satisfiability and the model-checking
problems are 2EXPTIME-COMPLETE, as they are for AT
Probabilistic Knowledge-Based Programs
International audienceWe introduce Probabilistic Knowledge-Based Programs (PKBPs), a new, compact representation of policies for factored partially observable Markov decision processes. PKBPs use branching conditions such as if the probability of Ď• is larger than p, and many more. While similar in spirit to value-based policies, PKBPs leverage the factored representation for more compactness. They also cope with more general goals than standard state-based rewards, such as pure information-gathering goals. Compactness comes at the price of reactivity, since evaluating branching conditions on-line is not polynomial in general. In this sense, PKBPs are complementary to other representations. Our intended application is as a tool for experts to specify policies in a natural, compact language, then have them verified automatically. We study succinctness and the complexity of verification for PKBPs
Temporal specifications with accumulative values
Recently, there has been an effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions. At the heart of quantitative objectives lies the accumulation of values along a computation. It is often the accumulated sum, as with energy objectives, or the accumulated average, as with mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric (or Boolean) variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point in time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire infinite computation. We study the border of decidability for such quantitative extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities with both prefix-accumulation assertions, or extending LTL with both path-accumulation assertions, results in temporal logics whose model-checking problem is decidable. Moreover, the prefix-accumulation assertions may be generalized with "controlled accumulation," allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that this branching-time logic is, in a sense, the maximal logic with one or both of the prefix-accumulation assertions that permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, such as CTL or LTL, makes the problem undecidable
Knowledge-Based Programs as Plans: Succinctness and the Complexity of Plan Existence
Knowledge-based programs (KBPs) are high-level protocols describing the
course of action an agent should perform as a function of its knowledge. The
use of KBPs for expressing action policies in AI planning has been surprisingly
overlooked. Given that to each KBP corresponds an equivalent plan and vice
versa, KBPs are typically more succinct than standard plans, but imply more
on-line computation time. Here we make this argument formal, and prove that
there exists an exponential succinctness gap between knowledge-based programs
and standard plans. Then we address the complexity of plan existence. Some
results trivially follow from results already known from the literature on
planning under incomplete knowledge, but many were unknown so far.Comment: 10 pages, Contributed talk at TARK 2013 (arXiv:1310.6382)
http://www.tark.or
On the Hybrid Extension of CTL and CTL+
The paper studies the expressivity, relative succinctness and complexity of
satisfiability for hybrid extensions of the branching-time logics CTL and CTL+
by variables. Previous complexity results show that only fragments with one
variable do have elementary complexity. It is shown that H1CTL+ and H1CTL, the
hybrid extensions with one variable of CTL+ and CTL, respectively, are
expressively equivalent but H1CTL+ is exponentially more succinct than H1CTL.
On the other hand, HCTL+, the hybrid extension of CTL with arbitrarily many
variables does not capture CTL*, as it even cannot express the simple CTL*
property EGFp. The satisfiability problem for H1CTL+ is complete for triply
exponential time, this remains true for quite weak fragments and quite strong
extensions of the logic
IST Austria Technical Report
There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with “controlled-accumulation”, allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable
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
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