Zachos received his PhD from the ETHZ (Swiss Federal Institute of Technology Zurich) in Mathematics (and Computer Science), 1978. He has held the posts of professor in Computer Science at UCSB, CUNY and NTUA and Adjunct professor at ETHZ. He has worked as a researcher at MIT, Brown-Boveri.
Stathis has published research papers in several areas of Computer Science. His work on Randomized Complexity Classes, Arthur–Merlin Games, and Interactive Proof Systems has been very influential in proving important theorems and is cited in main textbooks of computational complexity. One of his important contributions, using Interactive Proof Systems and Probabilistic Quantifiers, is that the Graph isomorphism Problem is not likely to be NP-complete (joint with R. Boppana, J. Hastad). Graph Isomorphism is one of the very few celebrated problems in NP that have not been shown yet to be either NP-Complete or in P. Zachos's most influential work was introducing and proving properties of the class Parity-P (with Christos Papadimitriou). He also introduced Probabilistic Quantifiers and Alternations of Probabilistic Quantifiers to uniformly describe various Complexity Classes as well as Interactive Proof Systems and Probabilistic Games.
His current interests include Probabilistic and Functional Complexity Classes, Combinatory Algebras as a foundation to Theory of Computations, the interconnections of Cryptographic Techniques and Computational Complexity as well as Algorithms for Graph Problems. He has co-organized International Conferences: STOC '87 (and programming committee of STOC '01), ICALP, CiE (Computability in Europe), PLS, ASL (Association for Symbolic Logic) European Summer Meeting, ACAC (Athens Colloquium on Algorithms and Complexity) and NYCAC (New York Colloquium on Algorithms and Complexity).
He is the brother of theoretical physicist Cosmas Zachos.
- Zachos, Stathis (1982). "Robustness of probabilistic computational complexity classes under definitional perturbations". Information and Control. 54 (3): 143–154. doi:10.1016/s0019-9958(82)80019-3.
- Zachos, Stathis; Hans Heller (1986). "A decisive characterization of BPP". Information and Control. 69 (1–3): 125–135. doi:10.1016/s0019-9958(86)80044-4.
- Zachos, Stathis; Martin Fürer (1987). Probabilistic quantifiers vs. distrustful adversaries. Foundations of Software Technology and Theoretical Computer Science. Lecture Notes in Computer Science. 287. pp. 443–455. doi:10.1007/3-540-18625-5_67. ISBN 978-3-540-18625-0.
- Fürer, Martin; Oded Goldreich; Yishay Mansour; Michael Sipser; Stathis Zachos (1989). "On completeness and soundness in interactive proof systems". Advances in Computing Research: Randomness and Computation. 5: 25–32. CiteSeerX 10.1.1.39.9412.
- Papadimitriou, Christos H. (1994). Computational Complexity. Addison Wesley.
- Hemaspaandra, Lane A.; Mitsunori Ogihara (2001). The Complexity Theory Companion. Springer. ISBN 978-3540674191.
- Du, Ding-Zhu; Ker-I Ko (2000). Theory of Computational Complexity. Wiley-Interscience.
- Boppana, Ravi B.; Hastad, Johan; Zachos, Stathis (6 May 1987). "Does co-NP have short interactive proofs?". Information Processing Letters. 25 (2): 127–132. doi:10.1016/0020-0190(87)90232-8.
- Papadimitriou, Christos H.; Stathis Zachos (1982). "Two remarks on the power of counting". In Proceedings of the 6th GI-Conference on Theoretical Computer Science. Lecture Notes in Computer Science. 145: 269–276. doi:10.1007/BFb0009651. ISBN 978-3-540-11973-9.
- Zachos, Stathis (1988). "Probabilistic quantifiers and games". Journal of Computer and System Sciences. 36 (3): 433–451. doi:10.1016/0022-0000(88)90037-2.