Herbert Weir Smyth, A Greek Grammar for Colleges

a. For the perfect or pluperfect active indicative the forms of the perfect active participle and εἰμί or ἦν may be used: as λελυκώς εἰμι for λέλυκα, λελυκὼς ἦν for ἐλελύκη. So βεβοηθηκότες ἦσαν for ἐβεβοηθήκεσαν (βοηθέω come to aid); εἰμὶ τεθηκὼς for τέθηκα I have placed; γεγραφὼς ἦν for ἐγεγράφη I had written; πεπονθὼς ἦν I had suffered. Such forms are more common in the pluperfect and in general denote state rather than action.

b. For the perfect active a periphrasis of the aorist participle and ἔχω is sometimes used, especially when a perfect active form with transitive meaning is lacking; as στήσα_ς ἔχω I have placed (ἕστηκα, intransitive, stand), ἐρασθεὶς ἔχω I have loved. So often because the aspirated perfect is not used, as ἔχεις ταράξα_ς thou hast stirred up. Cp. habeo with the perfect participle.

c. In the perfect active subjunctive and optative the forms in -κω and -κοιμι are very rare. In their place the perfect active participle with ὦ and εἴην is usually employed: λελυκὼς (λελοιπὼς) ὦ, εἴην. Other forms than 3 sing. and 3 pl. are rare. Cp. 691, 694.

d. The perfect or pluperfect passive is often paraphrased by the perfect participle and ἐστί or ἦν; as γεγραμμένον ἐστί it stands written, ἐστὶ δεδογμένον it stands resolved, παρηγγελμένον ἦν ῀ παρήγγελτο (παραγγέλλω give orders).

e. In the third plural of the perfect and pluperfect middle (passive) the perfect middle participle with εἰσί (ἦσαν) is used when a stem ending in a consonant would come in direct contact with the endings -νται, -ντο. See 408.

f. The perfect subjunctive and optative middle are formed by the perfect middle participle with ὦ or εἴην: λελυμένος ὦ, εἴην.

g. The perfect imperative of all voices may be expressed by combining the perfect participle with ἴσθι, ἔστω (697). λελυκὼς ἴσθι loose, etc., εἰρημένον ἔστω let it have been said, γεγονὼς ἔστω P. L. 951c, γεγονότες ἔστωσαν P. L. 779d.

h. Periphrasis of the infinitive is rare: ““τεθνηκότα εἶναι” to be dead” X. C. 1.4.11.