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### Incomplete Distinguishing Sequences for Finite State Machines

Robert M. Hierons, Uraz Cengiz Türker
2015 Computer journal
In this paper, we examine the problem of finding incomplete PDSs and ADSs, exploring associated optimisation problems: finding a largest set of states that has a DS and finding a smallest set of DSs that  ...  , between them, distinguish all of the states.  ...  To prove that the problem of approximating the MaxSubSetPDS is PSPACE-hard, let us assume that we have an algorithm P that belongs to a complexity class C < P SP ACE and returns an n ε approximation for  ...

### The Unbounded-Error Communication Complexity of Symmetric Functions

Alexander A. Sherstov
2008 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Put differently, we prove an optimal lower bound on the unbounded-error communication complexity of every symmetric function, i.e., a function of the form f (x, y) = D(|x ∧ y|) for some D.  ...  We determine the sign-rank of every matrix of the form M = [ D(|x ∧ y|) ] x,y , where D : {0, 1, . . . , n} → {−1, +1} is given and x and y range over {0, 1} n .  ...  Applied to our setting, it states that the sign-rank of F is proportional to the quantity min x,y |P x y | P • F , where • denotes entrywise multiplication and P = [P x y ] is any matrix whose entries  ...

### The unbounded-error communication complexity of symmetric functions

Alexander A. Sherstov
2011 Combinatorica
Put differently, we prove an optimal lower bound on the unbounded-error communication complexity of every symmetric function, i.e., a function of the form f (x, y) = D(|x ∧ y|) for some D.  ...  We determine the sign-rank of every matrix of the form M = [ D(|x ∧ y|) ] x,y , where D : {0, 1, . . . , n} → {−1, +1} is given and x and y range over {0, 1} n .  ...  Applied to our setting, it states that the sign-rank of F is proportional to the quantity min x,y |P x y | P • F , where • denotes entrywise multiplication and P = [P x y ] is any matrix whose entries  ...

### Infinite games with finite knowledge gaps [article]

Dietmar Berwanger, Anup Basil Mathew
2015 arXiv   pre-print
Instead, our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play.  ...  We show that it is decidable whether a given game satisfies the condition, and prove tight complexity bounds for the strategy synthesis problem under ω-regular winning conditions given by parity automata  ...  This work was supported by the European Union Seventh Framework Programme under Grant Agreement 601148 (CASSTING) and by the Indo-French Formal Methods Lab (LIA Informel).  ...

### A Glimpse at Paul G. Spirakis [chapter]

Ioannis Chatzigiannakis, Dimitris Fotakis, Spyros Kontogiannis, Othon Michail, Sotiris Nikoletseas, Grammati Pantziou, Christos Zaroliagis
2015 Lecture Notes in Computer Science
We are indebted to Eleni Spiraki (Paul's sister) for her great help in the preparation of this article.  ...  and the Greek State).  ...  This conversion has to preserve the assumed properties and limitations of the distributed computing model.  ...

### Editors: Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl; Article No. 141

Amanda Belleville, David Doty, David Soloveichik
2017 14 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik   unpublished
We also show that it requires linear time to exactly compute a wide range of semilinear functions (e.g., f (m) = m if m is even and 2m if m is odd) and predicates (e.g., parity, equality).  ...  Although the class of predicates and functions computable with probability 1 (stable computation) is the same whether a leader is required or not (semilinear functions and predicates), it is not known  ...  We are grateful to Sungjin Im for the proof of an important technical lemma, and we thank anonymous reviewers for very helpful comments.  ...

### Hardness of computing and approximating predicates and functions with leaderless population protocols [article]

Amanda Belleville, David Doty, David Soloveichik
2018 pre-print
Although the class of predicates and functions computable with probability 1 is the same whether or not there is an initial leader (semilinear functions and predicates), it is not known whether a leader  ...  We also show that it requires linear time to exactly compute a wide range of semilinear functions (e.g., f(m)=m if m is even and 2m if m is odd).  ...  The authors are grateful to Sungjin Im for the proof of Lemma 8.1. We also thank anonymous reviewers for their helpful comments.  ...

### Distributed control and game design: From strategic agents to programmable machines [article]

Dario Paccagnan
2019 pre-print
This thesis deals with the analysis and coordination of large scale systems without the need of a centralized authority.  ...  First, we compare the performance of an equilibrium allocation with that of an optimal allocation and propose conditions under which all equilibrium allocations are efficient.  ...  10 f G , f SV , f MC distribution rules introduced in (10.5) and Definition 24 xviii Complexity classes P deterministic polynomial time class N P nondeterministic polynomial time class PLS polynomial local  ...