scholarly journals Bisimulation equivalence of a BPP and a finite-state system can be decided in polynomial time

2005 ◽  
Vol 138 (3) ◽  
pp. 49-60
Author(s):  
Martin Kot ◽  
Zdeněk Sawa
Keyword(s):  
Polynomial Time ◽  
State System ◽  
Finite State ◽  
Bisimulation Equivalence

scholarly journals On the Complexity of Deciding Behavioural Equivalences and Preorders. A Survey

1996 ◽  
Vol 3 (39) ◽  
Author(s):  
Hans Hüttel ◽  
Sandeep Shukla
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Branching Time ◽  
Complexity Results ◽  
Special Cases ◽  
Finite State ◽  
Bisimulation Equivalence ◽  
Infinite State ◽  
Context Free

This paper gives an overview of the computational complexity of all the equivalences in the linear/branching time hierarchy [vG90a] and the preorders<br />in the corresponding hierarchy of preorders. We consider finite state or regular processes as well as infinite-state BPA [BK84b] processes. <br />A distinction, which turns out to be important in the finite-state processes, is that of simulation-like equivalences/preorders vs. trace-like equivalences<br />and preorders. Here we survey various known complexity results for these relations. For regular processes, all simulation-like equivalences and preorders are decidable in polynomial time whereas all trace-like equivalences and preorders are PSPACE-Complete. We also consider interesting special<br />classes of regular processes such as deterministic, determinate, unary, locally unary, and tree-like processes and survey the known complexity results in<br />these special cases. For infinite-state processes the results are quite different. For the class of context-free processes or BPA processes any preorder or equivalence beyond bisimulation is undecidable but bisimulation equivalence is polynomial time<br />decidable for normed BPA processes and is known to be elementarily decidable in the general case. For the class of BPP processes, all preorders and equivalences apart from bisimilarity are undecidable. However, bisimilarity<br />is decidable in this case and is known to be decidable in polynomial time for normed BPP processes.

scholarly journals Copyful Streaming String Transducers

2021 ◽  
Vol 178 (1-2) ◽  
pp. 59-76
Author(s):  
Emmanuel Filiot ◽  
Pierre-Alain Reynier
Keyword(s):  
Polynomial Time ◽  
Equivalence Problem ◽  
Expressive Power ◽  
The Other ◽  
Finite State Automata ◽  
Finite State ◽  
Variable Content ◽  
Deterministic Automata ◽  
Intermediate Output ◽  
Linear Manner

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Černý in 2010 as a one-way deterministic automata model to define transductions of finite strings. Copyless SST extend deterministic finite state automata with a set of variables in which to store intermediate output strings, and those variables can be combined and updated all along the run, in a linear manner, i.e., no variable content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transductions, and are as expressive as deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace). On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem. In this paper, we propose a semantics of HDT0L systems in terms of transductions, and use it to study the class of deterministic copyful SST. Our contributions are as follows: (i)HDT0L systems and total deterministic copyful SST have the same expressive power, (ii)the equivalence problem for deterministic copyful SST and the equivalence problem for HDT0L systems are inter-reducible, in quadratic time. As a consequence, equivalence of deterministic SST is decidable, (iii)the functionality of non-deterministic copyful SST is decidable, (iv)determining whether a non-deterministic copyful SST can be transformed into an equivalent non-deterministic copyless SST is decidable in polynomial time.

scholarly journals On Computational Tractability for Rational Verification

2019 ◽  
Author(s):  
Julian Gutierrez ◽  
Muhammad Najib ◽  
Giuseppe Perelli ◽  
Michael Wooldridge
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Multiagent Systems ◽  
Polynomial Time ◽  
Multiagent System ◽  
Reactive Systems ◽  
State System ◽  
Polynomial Space ◽  
Game Theoretic ◽  
Mean Payoff

Rational verification involves checking which temporal logic properties hold of a concurrent and multiagent system, under the assumption that agents in the system choose strategies in game theoretic equilibrium. Rational verification can be understood as a counterpart of model checking for multiagent systems, but while model checking can be done in polynomial time for some temporal logic specification languages such as CTL, and polynomial space with LTL specifications, rational verification is much more intractable: it is 2EXPTIME-complete with LTL specifications, even when using explicit-state system representations.  In this paper we show that the complexity of rational verification can be greatly reduced by restricting specifications to GR(1), a fragment of LTL that can represent most response properties of reactive systems. We also provide improved complexity results for rational verification when considering players' goals given by mean-payoff utility functions -- arguably the most widely used quantitative objective for agents in concurrent and multiagent systems. In particular, we show that for a number of relevant settings, rational verification can be done in polynomial space or even in polynomial time.

INFIX-FREE REGULAR EXPRESSIONS AND LANGUAGES

2006 ◽  
Vol 17 (02) ◽  
pp. 379-393 ◽  
Author(s):  
YO-SUB HAN ◽  
YAJUN WANG ◽  
DERICK WOOD
Keyword(s):  
Polynomial Time ◽  
Regular Language ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Regular Languages ◽  
Finite State Automaton ◽  
Primality Test ◽  
Finite State ◽  
State Pair ◽  
Free Decomposition

We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of a regular language using state-pair graphs. We consider two cases: 1) A language is specified by a nondeterministic finite-state automaton and 2) a language is specified by a regular expression. Furthermore, we examine the prime infix-free decomposition of infix-free regular languages and design an algorithm for the infix-free primality test of an infix-free regular language. Moreover, we show that we can compute the prime infix-free decomposition in polynomial time. We also demonstrate that the prime infix-free decomposition is not unique.

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